Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)

Metric Spaces of Non-Positive Curvature

Bridson, M. R., & Haefliger, A. (1999) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-662-12494-9 · Cited by 4,569

Markov Processes: Characterization and Convergence.

Abakuks, A., Ethier, S. N., & Kurtz, T. G. (1987) · Biometrics · doi:10.2307/2531839 · Cited by 4,471

Markov Processes

Ethier, S. N., & Kurtz, T. G. (1986) · Wiley series in probability and statistics · doi:10.1002/9780470316658 · Cited by 3,662

Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications

Mezard, M., Parisi, G., & Virasoro, M. (1986) · World Scientific Lecture Notes in Physics · doi:10.1142/0271 · Cited by 3,653

Inferring Phylogenies.

Wooding, S. (2004) · The American Journal of Human Genetics · doi:10.1086/383584 · Cited by 3,093

Foundations of Modern Probability

Kallenberg, O. (2021) · Probability theory and stochastic modelling · doi:10.1007/978-3-030-61871-1 · Cited by 2,918

A Course in Metric Geometry

Burago, D., Burago, Y., & Ivanov, S. (2001) · Graduate Studies in Mathematics · doi:10.1090/gsm/033 · Cited by 2,598

Foundations of Modern Probability

Kallenberg, O. (2002) · Probability and its applications · doi:10.1007/978-1-4757-4015-8 · Cited by 2,472

Gene genealogies and the coalescent process.

Hudson, R. R. (1990) · Medical Entomology and Zoology · Cited by 1,838

Metric Structures for Riemannian and Non-Riemannian Spaces

Gromov, M., Lafontaine, J., & Pansu, P. (2007) · Birkhäuser Boston eBooks · doi:10.1007/978-0-8176-4583-0 · Cited by 1,798

Gromov–Wasserstein Distances and the Metric Approach to Object Matching

Mémoli, F. (2011) · Foundations of Computational Mathematics · doi:10.1007/s10208-011-9093-5 · Cited by 519

Topological pattern recognition for point cloud data

Carlsson, G. (2014) · Acta Numerica · doi:10.1017/s0962492914000051 · Cited by 230

Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flowsPreprint

Gigli, N., Mondino, A., & Savaré, G. (2013) · HAL · Cited by 157

A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces

Abraham, R., Delmas, J., & Hoscheit, P. (2013) · Electronic Journal of Probability · doi:10.1214/ejp.v18-2116 · Cited by 121

Liouville quantum gravity and the Brownian map III: the conformal structure is determined

Miller, J., & Sheffield⋆, S. (2021) · Probability Theory and Related Fields · doi:10.1007/s00440-021-01026-8 · Cited by 116

Topological Data Analysis with Applications

Carlsson, G., & Vejdemo‐Johansson, M. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108975704 · Cited by 122

CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES

Ambrosio, L. (2019) · International Congress of Mathematicians (ICM) · doi:10.1142/9789813272880_0015 · Cited by 102

Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces

Blumberg, A. J., Gal, I., Mandell, M. A., & Pancia, M. (2014) · Foundations of Computational Mathematics · doi:10.1007/s10208-014-9201-4 · Cited by 94

The Gromov–Wasserstein distance between networks and stable network invariants

Chowdhury, S., & Mémoli, F. (2019) · Information and Inference A Journal of the IMA · doi:10.1093/imaiai/iaz026 · Cited by 73

Scaling limits of random trees and planar mapsPreprint

Gall, J. L., & Miermont, G. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1101.4856 · Cited by 67

Scaling Limit of Random Planar Quadrangulations with a Boundary∗Preprint

(2011) · Cited by 67

The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces

Sturm, K. (2023) · Memoirs of the American Mathematical Society · doi:10.1090/memo/1443 · Cited by 66

An axiomatic characterization of the Brownian map

Miller, J., & Sheffield⋆, S. (2021) · Journal de l’École polytechnique — Mathématiques · doi:10.5802/jep.155 · Cited by 66

A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecksPreprint

Birkner, M., Blath, J., Moehle, M., Steinruecken, M., & Tams, J. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0808.0412 · Cited by 66

Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows

Gigli, N., Mondino, A., & Savaré, G. (2015) · Proceedings of the London Mathematical Society · doi:10.1112/plms/pdv047 · Cited by 64

On the sphericity of scaling limits of random planar quadrangulations

Miermont, G. (2008) · Electronic Communications in Probability · doi:10.1214/ecp.v13-1368 · Cited by 62

Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Haas, B., Miermont, G., Pitman, J., & Winkel, M. (2008) · Cited by 62

Tree-valued resampling dynamics Martingale problems and applications

Greven, A., Pfaffelhuber, P., & Winter, A. (2012) · Probability Theory and Related Fields · doi:10.1007/s00440-012-0413-8 · Cited by 57

Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Haas, B., Miermont, G., Pitman, J., & Winkel, M. (2008) · The Annals of Probability · doi:10.1214/07-aop377 · Cited by 55

Tree-valued Fleming–Viot dynamics with mutation and selection

Depperschmidt, A., Greven, A., & Pfaffelhuber, P. (2012) · The Annals of Applied Probability · doi:10.1214/11-aap831 · Cited by 48

The hull process of the Brownian plane

Curien, N., & Gall, J. L. (2015) · Probability Theory and Related Fields · doi:10.1007/s00440-015-0652-6 · Cited by 43

The gap between Gromov-vague and Gromov–Hausdorff-vague topology

Athreya, S., Löhr, W., & Winter, A. (2016) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2016.02.009 · Cited by 43

Marked metric measure spaces

Depperschmidt, A., Greven, A., & Pfaffelhuber, P. (2011) · Electronic Communications in Probability · doi:10.1214/ecp.v16-1615 · Cited by 40

A new family of Markov branching trees: the alpha-gamma model

Chen, B., Ford, D., & Winkel, M. (2009) · Electronic Journal of Probability · doi:10.1214/ejp.v14-616 · Cited by 40

The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs

Bhamidi, S., van der Hofstad, R., & Sen, S. (2017) · Probability Theory and Related Fields · doi:10.1007/s00440-017-0760-6 · Cited by 40

Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree

Croydon, D. A. (2008) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/07-aihp153 · Cited by 37

Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositionsPreprint

Pitman, J., & Winkel, M. (2008) · Cited by 37

Invariance principle for variable speed random walks on treesPreprint

Athreya, S., & Winter, A. (2014) · Cited by 35

Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology

Gwynne, E., & Miller, J. (2017) · Electronic Journal of Probability · doi:10.1214/17-ejp102 · Cited by 34

Compactness theory of the space of Super Ricci flows

Bamler, R. H. (2023) · Inventiones mathematicae · doi:10.1007/s00222-023-01196-3 · Cited by 33

Invariance principle for variable speed random walks on trees

Athreya, S., Löhr, W., & Winter, A. (2017) · The Annals of Probability · doi:10.1214/15-aop1071 · Cited by 33

The cut-tree of large galton-watson trees and the brownian crt

Bertoin, J., & Miermont, G. (2013) · Zurich Open Repository and Archive (University of Zurich) · doi:10.5167/uzh-85277 · Cited by 31

Stability of 2-Parameter Persistent Homology

Blumberg, A. J., & Lesnick, M. (2022) · Foundations of Computational Mathematics · doi:10.1007/s10208-022-09576-6 · Cited by 25

The vertex-cut-tree of Galton–Watson trees converging to a stable tree

Dieuleveut, D. (2015) · The Annals of Applied Probability · doi:10.1214/14-aap1047 · Cited by 25

Regenerative tree growth: Binary self-similar continuum random trees and Poisson–Dirichlet compositions

Pitman, J., & Winkel, M. (2009) · The Annals of Probability · doi:10.1214/08-aop445 · Cited by 25

The cut-tree of large Galton–Watson trees and the Brownian CRT

Bertoin, J., & Miermont, G. (2013) · The Annals of Applied Probability · doi:10.1214/12-aap877 · Cited by 24

Universality for critical heavy-tailed network models: Metric structure of maximal components

Bhamidi, S., Dhara, S., van der Hofstad, R., & Sen, S. (2020) · Electronic Journal of Probability · doi:10.1214/19-ejp408 · Cited by 23

Exit times for an increasing Lévy tree-valued process

Abraham, R., Delmas, J., & Hoscheit, P. (2013) · Probability Theory and Related Fields · doi:10.1007/s00440-013-0509-9 · Cited by 22

The Effect of Single Recombination Events on Coalescent Tree Height and Shape

Luca Ferretti, A., Disanto, F., & Wiehe, T. (2013) · PLoS ONE · doi:10.1371/journal.pone.0060123 · Cited by 21

Continuum space limit of the genealogies of interacting Fleming-Viot processes on $\mathbb{Z}$

Greven, A., Sun, R., & Winter, A. (2016) · Electronic Journal of Probability · doi:10.1214/16-ejp4514 · Cited by 20

Distance distributions and inverse problems for metric measure spaces

Mémoli, F., & Needham, T. (2022) · Studies in Applied Mathematics · doi:10.1111/sapm.12526 · Cited by 22

The forest associated with the record process on a Lévy tree

Abraham, R., & Delmas, J. (2013) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2013.04.017 · Cited by 17

An invariance principle for branching diffusions in bounded domains

Powell, E. (2018) · Probability Theory and Related Fields · doi:10.1007/s00440-018-0847-8 · Cited by 17

Equivalence of Gromov-Prohorov- and Gromov's $\underline\Box_\lambda$-metric on the space of metric measure spaces

Loehr, W. (2013) · Electronic Communications in Probability · doi:10.1214/ecp.v18-2268 · Cited by 16

Convergence of mixing times for sequences of random walks on finite graphs

Croydon, D. A., Hambly, B. M., & Kumagai, T. (2012) · Electronic Journal of Probability · doi:10.1214/ejp.v17-1705 · Cited by 16

Geometry of the vacant set left by random walk on random graphs, Wright's constants, and critical random graphs with prescribed degrees

Bhamidi, S., & Sen, S. (2019) · Random Structures and Algorithms · doi:10.1002/rsa.20880 · Cited by 16

Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology

Gwynne, E., & Miller, J. (2017) · Apollo (University of Cambridge) · doi:10.17863/cam.14170 · Cited by 15

The Ultrametric Gromov–Wasserstein Distance

Mémoli, F., Munk, A., Wan, Z., & Weitkamp, C. A. (2023) · Discrete & Computational Geometry · doi:10.1007/s00454-023-00583-0 · Cited by 14

Brownian geometry

Gall, J. L. (2019) · Japanese journal of mathematics · doi:10.1007/s11537-019-1821-7 · Cited by 14

Existence of mark functions in marked metric measure spaces

Kliem, S., & Löhr, W. (2015) · Electronic Journal of Probability · doi:10.1214/ejp.v20-3969 · Cited by 14

The cut-tree of large recursive trees

Bertoin, J. (2015) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/13-aihp597 · Cited by 14

Hereditary tree growth and Lévy forests

Duquesne, T., & Winkel, M. (2018) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2018.10.007 · Cited by 14

The Aldous chain on cladograms in the diffusion limit

Löhr, W., Mytnik, L., & Winter, A. (2020) · The Annals of Probability · doi:10.1214/20-aop1431 · Cited by 14

Characterising rectifiable metric spaces using tangent spaces

Bate, D. (2022) · Inventiones mathematicae · doi:10.1007/s00222-022-01136-7 · Cited by 13

Convergence of bi-measure $\mathbb{R}$-trees and the pruning process

Löhr, W., Voisin, G., & Winter, A. (2015) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/14-aihp628 · Cited by 13

Genealogies and inference for populations with highly skewed offspring distributions

Birkner, M., & Blath, J. (2021) · EMS series of congress reports · doi:10.4171/ecr/17-1/8 · Cited by 12

Cutting down $\mathbf{p}$-trees and inhomogeneous continuum random trees

Broutin, N., & Wang, M. (2017) · Bernoulli · doi:10.3150/16-bej813 · Cited by 12

Scaling limits of the three-dimensional uniform spanning tree and associated random walk

Angel, O., Croydon, D. A., Hernández-Torres, S., & Shiraishi, D. (2021) · The Annals of Probability · doi:10.1214/21-aop1523 · Cited by 11

Convergence of non-bipartite maps via symmetrization of labeled trees

Addario‐Berry, L., & Albenque, M. (2021) · Annales Henri Lebesgue · doi:10.5802/ahl.84 · Cited by 11

Convergence of percolation on uniform quadrangulations with boundary to SLE$ _{6}$ on $ \sqrt{8/3}$-Liouville quantum gravity

Gwynne, E., & Miller, J. (2022) · Astérisque · doi:10.24033/ast.1152 · Cited by 11

Tree limits and limits of random trees

Janson, S. (2021) · Combinatorics Probability Computing · doi:10.1017/s0963548321000055 · Cited by 11

Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Miermont, G., Haas, B., Pitman, J., & Winkel, M. (2008) · Base Institutionnelle de Recherche de l'université Paris-Dauphine (BIRD) (University Paris-Dauphine) · Cited by 11

Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees

Chen, B., & Winkel, M. (2013) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/12-aihp533 · Cited by 11

Dynamics of lineages in adaptation to a gradual environmental change

Calvez, V., Henry, B., Méléard, S., & Tran, V. C. (2022) · Annales Henri Lebesgue · doi:10.5802/ahl.135 · Cited by 10

Global lower mass-bound for critical configuration models in the heavy-tailed regime

Bhamidi, S., Dhara, S., van der Hofstad, R., & Sen, S. (2022) · Electronic Journal of Probability · doi:10.1214/22-ejp821 · Cited by 10

Pathwise construction of tree-valued Fleming-Viot processes

Gufler, S. (2018) · Electronic Journal of Probability · doi:10.1214/18-ejp166 · Cited by 10

The Brownian continuum random tree as the unique solution to a fixed point equation

Albenque, M., & Goldschmidt, C. (2015) · Electronic Communications in Probability · doi:10.1214/ecp.v20-4250 · Cited by 9

Convergence of odd-angulations via symmetrization of labeled treesPreprint

Addario‐Berry, L., & Albenque, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.04786 · Cited by 9

On the Two Oldest Families for the Wright-Fisher Process

Delmas, J., Dhersin, J., & Siri‐Jégousse, A. (2010) · Electronic Journal of Probability · doi:10.1214/ejp.v15-771 · Cited by 8

Convergence and Limits of Finite Trees

Elek, G., & Tardos, G. (2021) · COMBINATORICA · doi:10.1007/s00493-021-4445-5 · Cited by 8

The semigroup of metric measure spaces and its infinitely divisible probability measures

Evans, S. N., & Molchanov, I. S. (2015) · Transactions of the American Mathematical Society · doi:10.1090/tran/6714 · Cited by 8

A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes

Gufler, S. (2018) · Electronic Journal of Probability · doi:10.1214/18-ejp153 · Cited by 8

Graphons, permutons and the Thoma simplex: three mod‐Gaussian moduli spaces

Féray, V., Méliot, P., & Nikeghbali, A. (2020) · Proceedings of the London Mathematical Society · doi:10.1112/plms.12344 · Cited by 8

Reversing the cut tree of the Brownian continuum random tree

Broutin, N., & Wang, M. (2017) · Electronic Journal of Probability · doi:10.1214/17-ejp105 · Cited by 8

Exit times for an increasing Lévy tree-valued processPreprint

Abraham, R., Delmas, J., & Hoscheit, P. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1202.5463 · Cited by 8

Regenerative tree growth: structural results and convergence

Pitman, J., Rizzolo, D., & Winkel, M. (2014) · Electronic Journal of Probability · doi:10.1214/ejp.v19-3040 · Cited by 7

Branching Processes - A General Concept

Greven, A., Rippl, T., & Glöede, P. (2021) · Latin American Journal of Probability and Mathematical Statistics · doi:10.30757/alea.v18-25 · Cited by 7

The SLE loop via conformal welding of quantum disks

Ang, M., Holden, N., & Sun, X. (2023) · Electronic Journal of Probability · doi:10.1214/23-ejp914 · Cited by 7

The total external length of the evolving Kingman coalescent

Dahmer, I., & Kersting, G. D. (2016) · Probability Theory and Related Fields · doi:10.1007/s00440-016-0703-7 · Cited by 7

Pruning of CRT-sub-trees

Abraham, R., Delmas, J., & He, H. X. (2014) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2014.11.008 · Cited by 7

Spaces of algebraic measure trees and triangulations of the circle

Löhr, W., & Winter, A. (2021) · Bulletin de la Société mathématique de France · doi:10.24033/bsmf.2825 · Cited by 7

Convergence of genealogies through spinal decomposition with an application to population genetics

Foutel‐Rodier, F., & Schertzer, E. (2023) · Probability Theory and Related Fields · doi:10.1007/s00440-023-01223-7 · Cited by 7

Continuum Space Limit of the Genealogies of Interacting Fleming-Viot Processes on $\Z$Preprint

Greven, A., Sun, R., & Winter, A. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1508.07169 · Cited by 7

Multiscale Analysis: Fisher–Wright Diffusions with Rare Mutations and Selection, Logistic Branching System

Dawson, D. A., & Greven, A. (2011) · Springer proceedings in mathematics · doi:10.1007/978-3-642-23811-6_15 · Cited by 6

Metrization of the Gromov–Hausdorff (-Prokhorov) topology for boundedly-compact metric spaces

Khezeli, A. (2019) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2019.11.001 · Cited by 6

Convergence of metric transformed spaces

Kazukawa, D. (2022) · Israel Journal of Mathematics · doi:10.1007/s11856-022-2348-9 · Cited by 6

Динамика метрик в пространствах с мерой и масштабированная энтропия

Вершик, А. М., Veprev, G. A., & Zatitskii, P. B. (2023) · Успехи математических наук · doi:10.4213/rm10103 · Cited by 6

Inverting the cut-tree transform

Addario‐Berry, L., Dieuleveut, D., & Goldschmidt, C. (2019) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/18-aihp921 · Cited by 6

A compact containment result for nonlinear historical superprocess approximations for population models with trait-dependence

Kliem, S. (2014) · Electronic Journal of Probability · doi:10.1214/ejp.v19-3506 · Cited by 6

Evolving phylogenies of trait-dependent branching with mutation and competition, Part I: Existence

Kliem, S., & Winter, A. (2018) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2018.07.011 · Cited by 6

Convergence of metric two-level measure spaces

Meizis, R. (2019) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2019.10.002 · Cited by 6

Fires on large recursive trees

Marzouk, C. (2015) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2015.08.006 · Cited by 6

Renormalisation of hierarchically interacting Cannings processesPreprint

Greven, A., den Hollander, F., Kliem, S., & Klimovsky, A. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1209.1856 · Cited by 6

Duality for spatially interacting Fleming-Viot processes with mutation and selectionPreprint

Dawson, D. A., & Greven, A. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1104.1099 · Cited by 6

Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Gadgil, S., & Krishnapur, M. (2012) · International Mathematics Research Notices · doi:10.1093/imrn/rns208 · Cited by 5

Scaling limit of random planar quadrangulations with a boundary

Bettinelli, J. (2015) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/13-aihp581 · Cited by 5

Path-properties of the tree-valued Fleming–Viot process

Depperschmidt, A., Greven, A., & Pfaffelhuber, P. (2013) · Electronic Journal of Probability · doi:10.1214/ejp.v18-2514 · Cited by 5

Characterizations of SLE$ _{\kappa}$ for $ \kappa \in (4,8)$ on Liouville quantum gravity

Gwynne, E., & Miller, J. (2022) · Astérisque · doi:10.24033/ast.1153 · Cited by 5

Exchangeable hierarchies and mass-structure of weighted real trees

Forman, N. (2020) · Electronic Journal of Probability · doi:10.1214/20-ejp522 · Cited by 5

Random cubic planar graphs converge to the Brownian sphere

Albenque, M., Fusy, É., & Lehéricy, T. (2023) · Electronic Journal of Probability · doi:10.1214/23-ejp912 · Cited by 5

Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees), Probab. Theory Related Fields 145Preprint

Greven, A., Pfaffelhuber, P., & Winter, A. (2009)

Convergence in distribution of random metric measure spaces: (Lambda-coalescent measure trees)Preprint

Greven, A., Pfaffelhuber, P., & Winter, A. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0609801 · Cited by 7

Compact metric measure spaces and Λ-coalescents coming down from infinity

Biehler, H. F., & Pfaffelhuber, P. (2012)

Compact metric measure spaces and Lambda-coalescents coming down from infinityPreprint

Biehler, H. F., & Pfaffelhuber, P. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1105.2409

Marked metric measure spaces

Depperschmidt, A., Greven, A., & Pfaffelhuber, P. (2011) · Electronic Communications in Probability · doi:10.1214/ecp.v16-1615 · Cited by 40