Central limit theorems for Gaussian polytopes
Open accessAbstract
Choose n random, independent points in Rd according to the standard normal distribution. Their convex hull Kn is the Gaussian random polytope. We prove that the volume and the number of faces of Kn satisfy the central limit theorem, settling a well-known conjecture in the field.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Due to the central limit theorem, the ICA estimates can be obtained by determining the directions for which the nongaussianity is maximum.
“Due to the well known central limit theorem (Barany, 2007), the ICA estimates can be obtained from the determination of the directions for which the nongaussianity is maximum.”
From Passive Sonar Signal Detection and Classification Based on Independent Component Analysis (2011) · cites this paper as Barany, 2007
The Abstract reports central limit theorems for the volume and number of faces of Gaussian random polytopes. Section 4 describes the general tendency of normalized sums toward a Gaussian distribution, but neither passage addresses ICA estimates or maximizing nongaussianity over directions. Searches for ICA and for projection directions found no passage supporting that inference. (LLM, conf=0.76)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Stein, C. (1972) · University of California Press eBooks · doi:10.1525/9780520423671-036 · Cited by 1,076 · see citing works
�ber die konvexe H�lle von n zuf�llig gew�hlten Punkten
R�nyi, A., & Sulanke, R. A. (1963) · Probability Theory and Related Fields · doi:10.1007/bf00535300 · Cited by 348 · see citing works
On Normal Approximations of Distributions in Terms of Dependency Graphs
Baldi, P., & Rinott, Y. (1989) · The Annals of Probability · doi:10.1214/aop/1176991178 · Cited by 116 · see citing works
Random projections of regular simplices
Affentranger, F., & Schneider, R. (1992) · Discrete & Computational Geometry · doi:10.1007/bf02187839 · Cited by 114 · see citing works
Limit theorems for convex hulls
Groeneboom, P. (1988) · Probability Theory and Related Fields · doi:10.1007/bf00342231 · Cited by 113 · see citing works
Central limit theorems for random polytopes
Reitzner, M. (2005) · Probability Theory and Related Fields · doi:10.1007/s00440-005-0441-8 · Cited by 88 · see citing works
Weil, W. R. R., & Wieacker, J. A. (1993) · Elsevier eBooks · doi:10.1016/b978-0-444-89597-4.50023-8 · Cited by 70 · see citing works
On normal approximation rates for certain sums of dependent random variables
Rinott, Y. (1994) · Journal of Computational and Applied Mathematics · doi:10.1016/0377-0427(94)90016-7 · Cited by 64 · see citing works
Sharp concentration of random polytopes
Vu, V. H. (2005) · Geometric and Functional Analysis · doi:10.1007/s00039-005-0541-8 · Cited by 61 · see citing works
Self-citationRegular simplices and Gaussian samples
Baryshnikov, Y. M., & Vitale, R. A. (1994) · Discrete & Computational Geometry · doi:10.1007/bf02574000 · Cited by 55 · see citing works
Limit theorems for functionals of convex hulls
Cabo, A. J., & Groeneboom, P. (1994) · Probability Theory and Related Fields · doi:10.1007/bf01204952 · Cited by 54 · see citing works
On the Asymptotic Distribution of the Area Outside a Random Convex Hull in a Disk
Hsing, T. (1994) · The Annals of Applied Probability · doi:10.1214/aoap/1177005069 · Cited by 50 · see citing works
Limit theorems for the convex hull of random points in higher dimensions
Hueter, I. (1999) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-99-02499-x · Cited by 48 · see citing works
Central limit theorems for random polytopes in a smooth convex set
Vu, V. (2005) · Advances in Mathematics · doi:10.1016/j.aim.2005.11.011 · Cited by 48 · see citing works
Self-citationThe convex hull of a normal sample
Hueter, I. (1994) · Advances in Applied Probability · doi:10.1017/s0001867800026653 · Cited by 39 · see citing works
Gaussian polytopes: variances and limit theorems
Hug, D., & Reitzner, M. (2005) · Advances in Applied Probability · doi:10.1017/s0001867800000197 · Cited by 35 · see citing works
Asymptotic mean values of Gaussian polytopes
Hug, D., Munsonius, G. O., & Reitzner, M. (2003) · Cited by 24 · see citing works
Few points to generate a random polytope
Bárány, I., & Dalla, L. (1997) · Mathematika · doi:10.1112/s0025579300012638 · Cited by 22 · see citing works
Self-citationSur L'enveloppe convexe des nuages de points aleatoires dans Rn . I
Raynaud, H. (1970) · Journal of Applied Probability · doi:10.1017/s0021900200026917 · Cited by 7 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Random Convex Hulls and Extreme Value Statistics
Majumdar, S. N., Comtet, A., & Randon‐Furling, J. (2009) · Journal of Statistical Physics · doi:10.1007/s10955-009-9905-z · Cited by 118 · see citing works
Definitions of Demand Flexibility for Aggregate Residential Loads
Sajjad, I. A., Chicco, G., & Napoli, R. (2016) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2016.2522961 · Cited by 107 · see citing works
Musah, M., Kong, Y., Mensah, I. A., Antwi, S. K., & Donkor, M. (2020) · Environmental Science and Pollution Research · doi:10.1007/s11356-020-08488-8 · Cited by 96 · see citing works
Performance Analysis of Underlay Cognitive Radio Nonorthogonal Multiple Access Networks
Arzykulov, S., Nauryzbayev, G., Tsiftsis, T. A., & Maham, B. (2019) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2019.2930553 · Cited by 93 · see citing works
Theoretical analysis of BER performance of nonlinearly amplified FBMC/OQAM and OFDM signals
Bouhadda, H., Shaïek, H., Roviras, D., Zayani, R., Medjahdi, Y., & Bouallègue, R. (2014) · EURASIP Journal on Advances in Signal Processing · doi:10.1186/1687-6180-2014-60 · Cited by 73 · see citing works
Random points and lattice points in convex bodies
Bárány, I. (2008) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-08-01210-x · Cited by 70 · see citing works
Self-citationZhang, W., Lederman, J. C., de Lima, T. F., Zhang, J., Bilodeau, S., Hudson, L., Tait, A. N., Shastri, B. J., & Prucnal, P. R. (2024) · Light Science & Applications · doi:10.1038/s41377-023-01362-5 · Cited by 60 · see citing works
MIRROR: Model Inversion for Deep Learning Network with High Fidelity
An, S., Tao, G., Xu, Q., Liu, Y., Shen, G., Yao, Y., Xu, J., & Zhang, X. (2022) · Network and Distributed System Security Symposium · doi:10.14722/ndss.2022.24335 · Cited by 48 · see citing works
Hug, D. (2012) · Lecture notes in mathematics · doi:10.1007/978-3-642-33305-7_7 · Cited by 47 · see citing works
Non-Coherent Massive MIMO Systems: A Constellation Design Approach
Xie, H., Xu, W., Ngo, H. Q., & Li, B. (2020) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2020.2978806 · Cited by 43 · see citing works
Expected intrinsic volumes and facet numbers of random beta‐polytopes
Kabluchko, Z., Temesvari, D., & Thaele, C. (2018) · Mathematische Nachrichten · doi:10.1002/mana.201700255 · Cited by 42 · see citing works
Peng, X., & Wu, Y. (2017) · Swarm and Evolutionary Computation · doi:10.1016/j.swevo.2017.03.001 · Cited by 39 · see citing works
Passive Sonar Signal Detection and Classification Based on Independent Component Analysis
de Moura, N. N., de Seixas, J. M., & Ramos, R. (2011) · Sonar Systems · doi:10.5772/18286 · Cited by 37 · see citing works
Sadeghi, B., & Cohen, D. R. (2023) · Ore Geology Reviews · doi:10.1016/j.oregeorev.2023.105660 · Cited by 37 · see citing works
A fast hybrid clustering technique based on local nearest neighbor using minimum spanning tree
Mishra, G., & Mohanty, S. K. (2019) · Expert Systems with Applications · doi:10.1016/j.eswa.2019.04.048 · Cited by 34 · see citing works
Small-Ball Probabilities for the Volume of Random Convex Sets
Paouris, G., & Pivovarov, P. (2013) · Discrete & Computational Geometry · doi:10.1007/s00454-013-9492-2 · Cited by 34 · see citing works
Bárány, I., & Reitzner, M. (2010) · The Annals of Probability · doi:10.1214/09-aop514 · Cited by 33 · see citing works
Self-citationA spectral-domain wave-to-wire model of wave energy converters
Tan, J., Tao, W., Laguna, A. J., Polinder, H., Xing, Y., & Miedema, S. A. (2023) · Applied Ocean Research · doi:10.1016/j.apor.2023.103650 · Cited by 29 · see citing works
NEXUS Network: Connecting the Preceding and the Following in Dialogue Generation
Shen, X., Su, H., Li, W., & Klakow, D. (2018) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/d18-1463 · Cited by 28 · see citing works
Recent Results on Random Polytopes
Schneider, R. (2008) · Bollettino Della Unione Matematica Italiana · Cited by 29 · see citing works
High-dimensional limit theorems for random vectors in ℓpn-balls
Kabluchko, Z., Prochno, J., & Thäle, C. (2017) · Communications in Contemporary Mathematics · doi:10.1142/s0219199717500924 · Cited by 28 · see citing works
Central limit theorems for Gaussian polytopes
Bárány, I., & Vu, V. (2008) · The Annals of Probability · doi:10.1214/07-aop378 · Cited by 27 · see citing works
Self-citationRen, J., Yan, Y., Zhao, H., Ma, P., Zabalza, J., Hussain, Z., Luo, S., Dai, Q., Zhao, S. J., Sheikh, A., et al. (2020) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2020.3027987 · Cited by 26 · see citing works
Convex hulls of random walks: Expected number of faces and face probabilities
Kabluchko, Z., Vysotsky, V., & Zaporozhets, D. (2017) · Advances in Mathematics · doi:10.1016/j.aim.2017.09.002 · Cited by 25 · see citing works
A central limit theorem for projections of the cube
Paouris, G., Pivovarov, P., & Zinn, J. (2013) · Probability Theory and Related Fields · doi:10.1007/s00440-013-0518-8 · Cited by 25 · see citing works
Variance asymptotics and scaling limits for Gaussian polytopes
Calka, P., & Yukich, J. E. (2014) · Probability Theory and Related Fields · doi:10.1007/s00440-014-0592-6 · Cited by 24 · see citing works
On the Dynamic Equilibrium in Homeostasis
Hegyi, G., Vincze, G., & Szász, A. (2012) · Open Journal of Biophysics · doi:10.4236/ojbiphy.2012.23009 · Cited by 24 · see citing works
Féray, V. (2018) · Electronic Journal of Probability · doi:10.1214/18-ejp222 · Cited by 23 · see citing works
Comment on "Clustering by fast search and find of density peaks"Preprint
Wang, S., Wang, D., Li, C., & Li, Y. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1501.04267 · Cited by 23 · see citing works
Testing a simple formula for calculating approximate intensity-duration-frequency curves
Benestad, R. E., Lutz, J., Dyrrdal, A. V., Haugen, J. E., Parding, K. M., & Dobler, A. (2020) · Environmental Research Letters · doi:10.1088/1748-9326/abd4ab · Cited by 21 · see citing works
Gaussian polytopes: A cumulant-based approach
Grote, J., & Thaele, C. (2018) · Journal of Complexity · doi:10.1016/j.jco.2018.03.001 · Cited by 21 · see citing works
Kim, S., & Park, J. (2018) · IEEE Access · doi:10.1109/access.2018.2884896 · Cited by 20 · see citing works
Financial development, inclusive growth, and environmental quality: emerging markets perspective
Annor, L. D. J., Robaina, M., & Vieira, E. F. S. (2023) · Environment Development and Sustainability · doi:10.1007/s10668-023-04198-6 · Cited by 19 · see citing works
Construction and Supervised Learning of Long-Term Grey Cognitive Networks
Nápoles, G., Salmeron, J. L., & Vanhoof, K. (2019) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2019.2913960 · Cited by 18 · see citing works
Prediction of spectral regrowth for FBMC-OQAM system using cumulants
Bulusu, S. S. K. C., Shaïek, H., & Roviras, D. (2014) · IEEE International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob) · doi:10.1109/wimob.2014.6962202 · Cited by 16 · see citing works
Estimation of Gap Between Current Language Models and Human Performance
Shen, X., Oualil, Y., Greenberg, C., Singh, M., & Klakow, D. (2017) · Interspeech (USB) · doi:10.21437/interspeech.2017-729 · Cited by 16 · see citing works
Yang, H. J., Gandhi, H., Shi, L., Kreuzer, H. W., Ostrom, N. E., & Hegg, E. L. (2011) · Rapid Communications in Mass Spectrometry · doi:10.1002/rcm.5298 · Cited by 15 · see citing works
Hall, K., Grinstead, A., Lewis, J. S., Mercer, C., Moore, A. P., & Ridehalgh, C. (2021) · Physical Therapy Reviews · doi:10.1080/10833196.2021.1935106 · Cited by 15 · see citing works
A multiple kernel density clustering algorithm for incomplete datasets in bioinformatics
Liao, L., Li, K., Li, K., Yang, C., & Tian, Q. (2018) · BMC Systems Biology · doi:10.1186/s12918-018-0630-6 · Cited by 13 · see citing works
Zhang, X., Cao, L., Shan, Y., Li, M., Wang, F., Wang, Q., Zhang, Y., & Chen, M. (2019) · Optical Engineering · doi:10.1117/1.oe.58.5.056114 · Cited by 13 · see citing works
Normalized shaping regularization for robust separation of blended data
Zhao, Q., Du, Q., Gong, X., Li, X., Fu, L., & Chen, Y. (2019) · Geophysics · doi:10.1190/geo2018-0557.1 · Cited by 11 · see citing works
A probabilistic approach to study the load variations in aggregated residential load patterns
Sajjad, I. A., Chicco, G., & Napoli, R. (2014) · Power Systems Computation Conference · doi:10.1109/pscc.2014.7038105 · Cited by 11 · see citing works
High-dimensional limit theorems for random vectors in ℓpn-balls. II
Kabluchko, Z., Prochno, J., & Thäle, C. (2019) · Communications in Contemporary Mathematics · doi:10.1142/s0219199719500731 · Cited by 11 · see citing works
A multivariate Gnedenko law of large numbers
Fresen, D. (2013) · The Annals of Probability · doi:10.1214/12-aop804 · Cited by 11 · see citing works
The mean width of random polytopes circumscribed around a convex body
Böröczky, K. J., Fodor, F., & Hug, D. (2010) · Repository KITopen (Karlsruhe Institute of Technology) · doi:10.5445/ir/1000134240 · Cited by 11 · see citing works
Lin, Q., Wang, Q., Chen, B., Ye, Y., Ma, L., & Tan, K. C. (2024) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2024.3467048 · Cited by 10 · see citing works
Non-Coherent Massive MIMO Systems: A Constellation Design Approach
Xu, W., Xie, H., & Ngo, H. Q. (2019) · International Conference on Communications · doi:10.1109/icc.2019.8761100 · Cited by 10 · see citing works
Intrinsic Volumes and Gaussian Polytopes: The Missing Piece of the Jigsaw
Bárány, I., & Thäle, C. (2017) · Documenta Mathematica · doi:10.4171/dm/598 · Cited by 10 · see citing works
Self-citationExpected volumes of Gaussian polytopes, external angles, and multiple order statistics
Kabluchko, Z., & Zaporozhets, D. (2018) · Transactions of the American Mathematical Society · doi:10.1090/tran/7708 · Cited by 10 · see citing works
Asymptotic Methods for Random Tessellations
Calka, P. (2012) · Lecture notes in mathematics · doi:10.1007/978-3-642-33305-7_6 · Cited by 10 · see citing works
MOD- CONVERGENCE AND PRECISE DEVIATIONSPreprint
Féray, V., Méliot, P., & Nikeghbali, A. (2014) · arXiv (Cornell University) · Cited by 10 · see citing works
1 A multivariate Gnedenko law of large numbersPreprint
Fresen, D. J., Nigel, I., & Kalton, J. (2016) · Cited by 10 · see citing works
Burnout in Assisted Reproduction Professionals: The Influence of Stressors in the Workplace
Urteaga, R., & Díaz, A. (2024) · Healthcare · doi:10.3390/healthcare12212136 · Cited by 9 · see citing works
Alsaadi, O., Alpkan, L., & Yıldız, B. (2024) · International Journal of Innovation Studies · doi:10.1016/j.ijis.2024.12.002 · Cited by 9 · see citing works
The Swarm Hierarchical Control System
Larkin, E., Akimenko, T., & Богомолов, А. В. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-36622-2_3 · Cited by 9 · see citing works
Araghi, S. N., Fontanili, F., Lamine, E., Okongwu, U., & Bénaben, F. (2022) · Intelligent Systems with Applications · doi:10.1016/j.iswa.2022.200071 · Cited by 9 · see citing works
Al‐Rubaye, G. A. (2023) · AEU - International Journal of Electronics and Communications · doi:10.1016/j.aeue.2023.154929 · Cited by 9 · see citing works
Variance estimates for random disc-polygons in smooth convex discs
Fodor, F., & Vígh, V. (2018) · Journal of Applied Probability · doi:10.1017/jpr.2018.76 · Cited by 9 · see citing works
Aircraft APU Starter Health Monitoring and Failure Prognostics
Lou, Q. (2013) · doi:10.22215/etd/2013-09948 · Cited by 9 · see citing works
Facets of spherical random polytopes
Bonnet, G., & O’Reilly, E. (2022) · Mathematische Nachrichten · doi:10.1002/mana.202000314 · Cited by 8 · see citing works
ESTUDO SOBRE A AUTO-ESTIMA EM ADOLESCENTES DOS 12 AOS 17 ANOS
Feliciano, I. P., & Afonso, R. M. (2012) · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · Cited by 7 · see citing works
Automatic density clustering with multiple kernels for high-dimension bioinformatics data
Liao, L., Li, K., Li, K., Tian, Q., & Yang, C. (2017) · IEEE International Conference on Bioinformatics and Biomedicine (BIBM) · doi:10.1109/bibm.2017.8217984 · Cited by 7 · see citing works
A new approach to weak convergence of random cones and polytopes
Kabluchko, Z., Temesvari, D., & Thäle, C. (2020) · Canadian Journal of Mathematics · doi:10.4153/s0008414x20000620 · Cited by 7 · see citing works
Smoothed complexity of convex hulls by witnesses and collectors
Devillers, O., Glisse, M., Goaoc, X., & Thomasse, R. (2016) · Journal of computational geometry · doi:10.20382/jocg.v7i2a6 · Cited by 7 · see citing works
Random Sets and Random Functions
Molchanov, I. S. (2017) · Probability theory and stochastic modelling · doi:10.1007/978-1-4471-7349-6_5 · Cited by 7 · see citing works
Benestad, R. E., Lussana, C., & Dobler, A. (2024) · Discover Water · doi:10.1007/s43832-024-00063-3 · Cited by 5 · see citing works
Lajnef, H., Dakhli, M. C., Hizem, M., & Bouallègue, R. (2016) · International Wireless Communications and Mobile Computing Conference (IWCMC) · doi:10.1109/iwcmc.2016.7577219 · Cited by 6 · see citing works
Kim, I., Kim, H., & Kim, Y. (2019) · Nuclear Science and Engineering · doi:10.1080/00295639.2019.1654815 · Cited by 6 · see citing works
Thin-shell theory for rotationally invariant random simplices
Heiny, J., Johnston, S. G. G., & Prochno, J. (2022) · Electronic Journal of Probability · doi:10.1214/21-ejp734 · Cited by 6 · see citing works
Strack, K. M., Davydycheva, S., Passalacqua, H., Smirnov, M. Y., & Xu, X. (2021) · Journal of Marine Science and Engineering · doi:10.3390/jmse9080906 · Cited by 6 · see citing works
Mod-phi convergence I: Normality zones and precise deviationsPreprint
Féray, V., Méliot, P., & Nikeghbali, A. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1304.2934 · Cited by 6 · see citing works
Limit theorems for random points in a simplex
Baci, A., Kabluchko, Z., Prochno, J., Sonnleitner, M., & Thäle, C. (2022) · Journal of Applied Probability · doi:10.1017/jpr.2021.77 · Cited by 5 · see citing works
A theory of capacity and sparse neural encoding
Baldi, P., & Vershynin, R. (2021) · Neural Networks · doi:10.1016/j.neunet.2021.05.005 · Cited by 5 · see citing works
Support Recovery for Sparse Multidimensional Phase Retrieval
Novikov, A., & White, S. (2021) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2021.3096796 · Cited by 5 · see citing works
Zhang, C., Luo, C., Zhang, X., Tang, S., Ding, C., Awan, I. A., Tong, S., Ding, H., Xiao, T., Zou, N., et al. (2025) · Optics Express · doi:10.1364/oe.559338 · Cited by 4 · see citing works
Prado, I. F., Costa, F. B., Silva, K. M., de Medeiros, R. P., & Mork, B. A. (2024) · IEEE Access · doi:10.1109/access.2024.3456040 · Cited by 4 · see citing works
A Novel Framework for Learning Automata: A Statistical Hypothesis Testing Approach
Di, C., Li, S., Li, F., & Qi, K. (2019) · IEEE Access · doi:10.1109/access.2019.2901941 · Cited by 4 · see citing works
Convex Decreasing Algorithms: Distributed Synthesis and Finite-Time Termination in Higher Dimension
Melbourne, J., Saraswat, G., Khatana, V., Patel, S., & Salapaka, M. V. (2023) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2023.3344721 · Cited by 4 · see citing works
Gong, Y., & Cui, C. (2021) · Radioengineering · doi:10.13164/re.2021.0407 · Cited by 4 · see citing works
Identification of a cantilever beam’s spatially uncertain stiffness
Hoppe, K.-A., Kronthaler, M. G. T., Sepahvand, K. K., & Marburg, S. (2023) · Scientific Reports · doi:10.1038/s41598-023-27755-5 · Cited by 4 · see citing works
STATE: A Clustering Algorithm Focusing on Edges Instead of Centers
Zhao, B., Shuliang, W., & Liu, C. (2021) · Chinese Journal of Electronics · doi:10.1049/cje.2021.07.001 · Cited by 4 · see citing works
Wu, L., Chen, W., Deng, H.-H., Zhang, J., & Li, Y. (2016) · International Conference on Advanced Computational Intelligence (ICACI) · doi:10.1109/icaci.2016.7449844 · Cited by 4 · see citing works
High-dimensional limit theorems for random vectors in $\ell_p^n$-ballsPreprint
Kabluchko, Z., Prochno, J., & Thaele, C. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1709.09470 · Cited by 4 · see citing works
Yan, J., Xue, P., Li, W., You, L., Zhu, X., & Zhang, L. (2025) · Materials Science and Engineering A · doi:10.1016/j.msea.2025.149311 · Cited by 3 · see citing works
Morillas, J. M. B., González, D. M., & Gozalo, G. R. (2024) · Applied Acoustics · doi:10.1016/j.apacoust.2024.110195 · Cited by 3 · see citing works
Asymptotics of the convex hull of spherically symmetric samples
Hashorva, E. (2010) · Discrete Applied Mathematics · doi:10.1016/j.dam.2010.10.017 · Cited by 3 · see citing works
Dependency graphs and mod-Gaussian convergence
Féray, V., Méliot, P., & Nikeghbali, A. (2016) · SpringerBriefs in probability and mathematical statistics · doi:10.1007/978-3-319-46822-8_9 · Cited by 3 · see citing works
Laplacian Centrality Peaks Clustering Based on Potential Entropy
Yang, X.-H., Jin, L., Ye, W., Xiao, J., Zhang, D., & Xu, X. (2018) · IEEE Access · doi:10.1109/access.2018.2871500 · Cited by 3 · see citing works
Facets of High-Dimensional Gaussian Polytopes
Böröczky, K. J., Lugosi, G., & Reitzner, M. (2024) · Journal of Geometric Analysis · doi:10.1007/s12220-023-01440-5 · Cited by 3 · see citing works
Finding the Optimal Sample Based on Shannon’s Entropy and Genetic Algorithms
Aldana-Bobadilla, E., & Alfaro-Pérez, C. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-27060-9_29 · Cited by 3 · see citing works
Gaussian Convex Bodies: a Nonasymptotic Approach
Paouris, G., Pivovarov, P., & Valettas, P. (2019) · Journal of Mathematical Sciences · doi:10.1007/s10958-019-04256-3 · Cited by 3 · see citing works
Basani, J. R., & Bhattacherjee, A. (2021) · Communications in Computational Physics · doi:10.4208/cicp.oa-2020-0173 · Cited by 3 · see citing works
An Improved Clustering Algorithm Based on Density Peak and Nearest Neighbors
Zhao, C., Yang, J., & Wen, K. (2022) · Mathematical Problems in Engineering · doi:10.1155/2022/5499213 · Cited by 3 · see citing works
Molchanov, I. S. (2017) · Probability theory and stochastic modelling · doi:10.1007/978-1-4471-7349-6_2 · Cited by 2 · see citing works
Lo, C. N., Teo, V. Y. E., Manaff, N. F. A. B. A., Seow, T. C. Y., Harve, K. S., & Leung, B. P. L. (2024) · Healthcare · doi:10.3390/healthcare12181861 · Cited by 2 · see citing works
BUDS+: Better Privacy with Converger and Noisy Shuffling
Sengupta, P., Paul, S., & Mishra, S. (2021) · Digital Threats Research and Practice · doi:10.1145/3491259 · Cited by 2 · see citing works
Random Closed Sets and Capacity Functionals
Molchanov, I. S. (2017) · Probability theory and stochastic modelling · doi:10.1007/978-1-4471-7349-6_1 · Cited by 2 · see citing works
On the Expected Complexity of Maxout NetworksPreprint
Tseran, H., & Montúfar, G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.00379 · Cited by 2 · see citing works
Gusakova, A., Reitzner, M., & Thäle, C. (2023) · Annales Henri Lebesgue · doi:10.5802/ahl.180 · Cited by 1 · see citing works
- Authors
- Bárány, I., & Vu, V.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- ORCID
- Venue
- The Annals of Probability
- Publisher
- Institute of Mathematical Statistics
- Published
- 2007-07-01
- Volume
- 35
- Issue
- 4
- Pages
- 1593-1621
- ISSN
- 0091-1798 (ISSN-L)
- 2168-894X
- OpenAlex
- W2077846610
- Cited by
- 140
- References
- 19
- Citations by year
- 2025: 7 · 2024: 16 · 2023: 10 · 2022: 8 · 2021: 9 · 2020: 8 · 2019: 12 · 2018: 12 · 2017: 14 · 2016: 7 · 2015: 4 · 2014: 9 · 2013: 5 · 2012: 7
- FWCI
- 5.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Probability (publishedVersion)
- Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) (acceptedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Point processes and geometric inequalities
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- central limit theorem, convex hull, asymptotic normality
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
