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Lectures on finite Markov chains
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Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
An introduction to probability theory and its applications
(1958) · Journal of the Franklin Institute · doi:10.1016/0016-0032(58)90688-4 · Cited by 29,269
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 10,280
Horn, R. A., & Johnson, C. R. (1991) · Cambridge University Press eBooks · doi:10.1017/cbo9780511840371 · Cited by 9,319
An Introduction to Probability Theory and Its Applications.
Bharucha-Reid, A. T., & Feller, W. (1967) · The American Mathematical Monthly · doi:10.2307/2314609 · Cited by 6,066
Introduction to Fourier Analysis on Euclidean Spaces.
Stein, E. M., & Weiss, G. (1971) · Cited by 5,080
Approximation Algorithms for NP-Hard Problems
(1997) · ACM SIGACT News · doi:10.1145/261342.571216 · Cited by 3,103
Nonuniversal critical dynamics in Monte Carlo simulations
Swendsen, R. H., & Wang, J.-S. (1987) · Physical Review Letters · doi:10.1103/physrevlett.58.86 · Cited by 2,844
Non-negative Matrices and Markov Chains
Seneta, E. (1981) · Springer Series in Statistics · doi:10.1007/0-387-32792-4 · Cited by 2,807
Heat Kernels and Spectral Theory
Davies, E. B. (1989) · Cambridge University Press eBooks · doi:10.1017/cbo9780511566158 · Cited by 2,363
Logarithmic Sobolev Inequalities
Gross, L. (1975) · American Journal of Mathematics · doi:10.2307/2373688 · Cited by 1,755
Huber, P. J. (1997) · Springer Series in Statistics · doi:10.1007/978-1-4612-0667-5_6 · Cited by 1,551
Bush, K. A., Kemeny, J. G., & Snell, J. L. (1960) · The American Mathematical Monthly · doi:10.2307/2309264 · Cited by 1,546
Group representations in probability and statistics
Diaconis, P. (1988) · doi:10.1214/lnms/1215467407 · Cited by 1,381
Alon, N. (1986) · Combinatorica · doi:10.1007/bf02579166 · Cited by 1,137
Deuschel, J. (1989) · Cited by 1,120
A Lower Bound for the Smallest Eigenvalue of the Laplacian
Cheeger, J. (2015) · Problems in Analysis: A Symposium in Honor of Salomon Bochner (PMS-31) · doi:10.1515/9781400869312-013 · Cited by 961
Geometric Bounds for Eigenvalues of Markov Chains
Diaconis, P., & Stroock, D. (1991) · The Annals of Applied Probability · doi:10.1214/aoap/1177005980 · Cited by 882
λ1, Isoperimetric inequalities for graphs, and superconcentrators
Alon, N., & Milman, V. D. (1985) · Journal of Combinatorial Theory, Series B · doi:10.1016/0095-8956(85)90092-9 · Cited by 839
The IMA volumes in mathematics and its applications
Friedman, A., & Miller, W. (1986) · Springer eBooks · Cited by 648
Generating a random permutation with random transpositions
Diaconis, P., & Shahshahani, M. (1981) · Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete · doi:10.1007/bf00535487 · Cited by 575
Polynomial-Time Approximation Algorithms for the Ising Model
Jerrum, M., & Sinclair, A. (1993) · SIAM Journal on Computing · doi:10.1137/0222066 · Cited by 548
Improved Bounds for Mixing Rates of Markov Chains and Multicommodity Flow
Sinclair, A. (1992) · Combinatorics, Probability and Computing · doi:10.1017/s0963548300000390 · Cited by 498
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Jerrum, M., & Sinclair, A. (1996) · Cited by 489
Logarithmic Sobolev inequalities for finite Markov chains
Diaconis, P., & Saloff-Coste, L. (1996) · The Annals of Applied Probability · doi:10.1214/aoap/1034968224 · Cited by 479
Self-citationRandom walks on finite groups and rapidly mixing markov chains
Aldous, D. (1983) · Lecture notes in mathematics · doi:10.1007/bfb0068322 · Cited by 450
Comparison Theorems for Reversible Markov Chains
Diaconis, P., & Saloff-Coste, L. (1993) · The Annals of Applied Probability · doi:10.1214/aoap/1177005359 · Cited by 423
Self-citationRandom walks in a convex body and an improved volume algorithm
Lovász, L., & Simonovits, M. (1993) · Random Structures & Algorithms · doi:10.1002/rsa.3240040402 · Cited by 409
Algorithms for Random Generation and Counting: A Markov Chain Approach
Sinclair, A. (1993) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-0323-0 · Cited by 380
Fill, J. A. (1991) · The Annals of Applied Probability · doi:10.1214/aoap/1177005981 · Cited by 320
The cutoff phenomenon in finite Markov chains.
Diaconis, P. W. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.4.1659 · Cited by 306
Lawler, G. F., & Sokal, A. D. (1988) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1988-0930082-9 · Cited by 265
Strong Stationary Times Via a New Form of Duality
Diaconis, P., & Fill, J. A. (1990) · The Annals of Probability · doi:10.1214/aop/1176990628 · Cited by 253
Strong uniform times and finite random walks
Aldous, D., & Diaconis, P. (1987) · Advances in Applied Mathematics · doi:10.1016/0196-8858(87)90006-6 · Cited by 233
Comparison Techniques for Random Walk on Finite Groups
Diaconis, P., & Saloff-Coste, L. (1993) · The Annals of Probability · doi:10.1214/aop/1176989013 · Cited by 194
Self-citationAsymptotic analysis of a random walk on a hypercube with many dimensions
Diaconis, P., Graham, R. L., & Morrison, J. A. (1990) · Random Structures & Algorithms · doi:10.1002/rsa.3240010105 · Cited by 161
Rectangular Arrays with Fixed Margins
Diaconis, P., & Gangolli, A. (1995) · The IMA Volumes in Mathematics and its Applications · doi:10.1007/978-1-4612-0801-3_3 · Cited by 160
Time to Reach Stationarity in the Bernoulli–Laplace Diffusion Model
Diaconis, P., & Shahshahani, M. (1987) · SIAM Journal on Mathematical Analysis · doi:10.1137/0518016 · Cited by 160
What Do We Know about the Metropolis Algorithm ?
Diaconis, P. W., & Saloff‐Coste, L. (1998) · Journal of Computer and System Sciences · doi:10.1006/jcss.1998.1576 · Cited by 142
Self-citationChernoff-type bound for finite Markov chains
Lezaud, P. (1998) · The Annals of Applied Probability · doi:10.1214/aoap/1028903453 · Cited by 137
Aldous, D. (1987) · Probability in the Engineering and Informational Sciences · doi:10.1017/s0269964800000267 · Cited by 133
The Subgroup Algorithm for Generating Uniform Random Variables
Diaconis, P. W., & Shahshahani, M. (1987) · Probability in the Engineering and Informational Sciences · doi:10.1017/s0269964800000255 · Cited by 119
Nash inequalities for finite Markov chains
Diaconis, P. W., & Saloff‐Coste, L. (1996) · Journal of Theoretical Probability · doi:10.1007/bf02214660 · Cited by 107
Self-citationAnalytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
Rothaus, O. S. (1985) · Journal of Functional Analysis · doi:10.1016/0022-1236(85)90079-5 · Cited by 97
Random Shuffles and Group Representations
Flatto, L., Odlyzko, A. M., & Wales, D. B. (1985) · The Annals of Probability · doi:10.1214/aop/1176993073 · Cited by 81
Moderate growth and random walk on finite groups
Diaconis, P. W., & Saloff‐Coste, L. (1994) · Geometric and Functional Analysis · doi:10.1007/bf01898359 · Cited by 71
Self-citationMarkov chains and polynomial time algorithms
Kannan, R. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365726 · Cited by 63
Eigenvalues of Graphs and Sobolev Inequalities
Chung, F. R., & Yau, S. (1995) · Combinatorics Probability Computing · doi:10.1017/s0963548300001449 · Cited by 58
Walks on generating sets of Abelian groups
Diaconis, P. W., & Saloff‐Coste, L. (1996) · Probability Theory and Related Fields · doi:10.1007/bf01192214 · Cited by 42
Self-citationA Probability Inequality for the Occupation Measure of a Reversible Markov Chain
Dinwoodie, I. H. (1995) · The Annals of Applied Probability · doi:10.1214/aoap/1177004826 · Cited by 38
Generating Random Elements in SL n (F q ) by Random Transvections
Hildebrand, M. (1992) · Journal of Algebraic Combinatorics · doi:10.1023/a:1022472220105 · Cited by 34
What do we know about the Metropolis algorithm?
Diaconis, P. W., & Saloff‐Coste, L. (1995) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/225058.225095 · Cited by 31
Self-citationDiaconis, P. W., & Holmes, S. (1995) · The IMA volumes in mathematics and its applications · doi:10.1007/978-1-4612-0801-3_4 · Cited by 23
Random Walks on the Groups of Upper Triangular Matrices
Stong, R. (1995) · The Annals of Probability · doi:10.1214/aop/1176987809 · Cited by 18
Eigenvalues of Random Walks on Groups
Stong, R. (1995) · The Annals of Probability · doi:10.1214/aop/1176987811 · Cited by 9
Cited by
Gossip-based computation of aggregate information
Kempe, D., Dobra, A., & Gehrke, J. (2004) · 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings. · doi:10.1109/sfcs.2003.1238221 · Cited by 1,480
Stability results for Harnack inequalities
Grigor'yan, A., & Saloff-Coste, L. (2005) · Annales de l'Institut Fourier · doi:10.5802/aif.2116 · Cited by 99
Self-citation
Metadata
- Authors
- Saloff-Coste, L.
- Venue
- Lecture Notes in Mathematics
- Publisher
- Springer Berlin Heidelberg
- Published
- 1997
- Pages
- 301-413
- ISSN
- 0075-8434 (ISSN-L)
- 1617-9692
- OpenAlex
- W2237678354
- Cited by
- 382
- References
- 56
- FWCI
- 51.51
- Type
- book chapter
- Language
- en
- Open access
- closed
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