Brownian geometry: at the interface between probability theory, combinatorics and mathematical physics.

Project Information

GeoBrown

Grant agreement ID: 740943

DOI 10.3030/740943

Project closed

EC signature date 25 April 2017

Start date 1 May 2017

End date 30 April 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 263 607,00

EU contribution € 1 263 607,00

Coordinated by

UNIVERSITE PARIS-SACLAY
France

Publications

Peer reviewed articles (32)

A combinatorial proof of Aldous-Broder theorem for general Markov chains

Author(s): Luis Fredes, Jean-François Marckert
Published in: Random Structures and Algorithms, Issue 62, 2022, Page(s) 430-449, ISSN 1098-2418
Publisher: Wiley
DOI: 10.1002/rsa.21101

The phase transition for parking on Galton-Watson trees

Author(s): Nicolas Curien, Olivier Hénard
Published in: Discrete Analysis, Issue 1, 2022, ISSN 2397-3129
Publisher: Alliance of Diamond Open Access Journals
DOI: 10.19086/da.33167

The mesoscopic geometry of sparse random maps

Author(s): Nicolas Curien, Igor Kortchemski, Cyril Marzouk
Published in: Journal de l'Ecole Polytechnique, Issue 9, 2022, Page(s) 1305-1345, ISSN 2429-7100
Publisher: Editions de l'Ecole Polytechnique
DOI: 10.5802/jep.207

Markovian explorations of random planar maps are roundish

Author(s): Nicolas Curien, Cyril Marzouk
Published in: Bulletin de la Société mathématique de France, Issue 148/4, 2020, Page(s) 709-732, ISSN 0037-9484
Publisher: Societe Mathematique de France
DOI: 10.24033/bsmf.2821

The Markov property of local times of Brownian motion indexed by the Brownian tree

Author(s): Jean-François Le Gall
Published in: The Annals of Probability, 2024, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics

Iterated Brownian motion ad libitum is not the pseudo-arc

Author(s): Jérôme Casse, Nicolas Curien
Published in: Confluentes Mathematici, Issue 13, 2021, Page(s) 35-42, ISSN 1793-7442
Publisher: Centre Mersenne
DOI: 10.5802/cml.70

First-passage percolation and local modifications of distances in random triangulations

Author(s): Nicolas Curien, Jean-François Le Gall
Published in: Annales Scientifiques de l'Ecole Normale Supérieure, Issue 52, 2019, Page(s) 631-701, ISSN 0012-9593
Publisher: Elsevier BV
DOI: 10.24033/asens.2394

Local limits of uniform triangulations in high genus

Author(s): Thomas Budzinski, Baptiste Louf
Published in: Inventiones mathematicae, Issue 223/1, 2021, Page(s) 1-47, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-020-00986-3

Isoperimetric inequalities in the Brownian plane

Author(s): Riera, Armand
Published in: The Annals of Probability, 2023, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aop1576

Enumeration of Planar Constellations with an Alternating Boundary

Author(s): Jérémie Bouttier, Ariane Carrance
Published in: The Electronic Journal of Combinatorics, Issue 28/3, 2021, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/10149

The Brownian disk viewed from a boundary point

Author(s): Jean-François Le Gall
Published in: Annales de l'Institut Henri Poincaré Probabilités Statistiques, Issue 58/2, 2022, Page(s) 1091-1119, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/21-aihp1179

Recurrence of the uniform infinite half-plane map via duality of resistances

Author(s): Budzinski, Thomas; Leh��ricy, Thomas
Published in: The Annals of Probability, Issue 50, 2022, Page(s) 1725-1754, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-aop1539

Brownian disks and the Brownian snake

Author(s): Jean-François Le Gall
Published in: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Issue 55/1, 2019, Page(s) 237-313, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/18-aihp882

Subordination of trees and the Brownian map

Author(s): Jean-François Le Gall
Published in: Probability Theory and Related Fields, Issue 171/3-4, 2018, Page(s) 819-864, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-017-0794-9

Brownian geometry

Author(s): Jean-François Le Gall
Published in: Japanese Journal of Mathematics, Issue 14/2, 2019, Page(s) 135-174, ISSN 0289-2316
Publisher: Kinokuniya Co., Ltd.
DOI: 10.1007/s11537-019-1821-7

Separating cycles and isoperimetric inequalities in the uniform infinite planar quadrangulation

Author(s): Jean-François Le Gall, Thomas Lehéricy
Published in: The Annals of Probability, Issue 47/3, 2019, Page(s) 1498-1540, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/18-aop1289

Some explicit distributions for Brownian motion indexed by the Brownian tree

Author(s): Jean-François Le Gall, Armand Riera
Published in: Markov Processes and Related Fields, 2020, ISSN 1024-2953
Publisher: Polymat

Growth-fragmentation processes in Brownian motion indexed by the Brownian tree

Author(s): Jean-François Le Gall, Armand Riera
Published in: The Annals of Probability, 2020, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics

Universality for Random Surfaces in Unconstrained Genus

Author(s): Thomas Budzinski, Nicolas Curien, Bram Petri
Published in: The Electronic Journal of Combinatorics, Issue 26/4, 2019, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/8623

Supercritical causal maps: geodesics and simple random walk

Author(s): Thomas Budzinski
Published in: Electronic Journal of Probability, Issue 24/0, 2019, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-EJP341

Strict monotonicity of percolation thresholds under covering maps

Author(s): Sébastien Martineau, Franco Severo
Published in: The Annals of Probability, 2020, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics

Geometric and spectral properties of causal maps

Author(s): Nicolas Curien, Tom Hutchcroft, Asaf Nachmias
Published in: Journal of the European Mathematical Society, 2020, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House

How fast planar maps get swallowed by a peeling process

Author(s): Nicolas Curien, Cyril Marzouk
Published in: Electronic Communications in Probability, Issue 23, 2018, ISSN 1083-589X
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/18-ecp123

Duality of random planar maps via percolation

Author(s): Nicolas Curien, Loïc Richier
Published in: Annales de l'Institut Fourier, 2020, ISSN 1777-5310
Publisher: Centre Mersenne

The skeleton of the UIPT, seen from infinity

Author(s): Nicolas Curien, Laurent Ménard
Published in: Annales Henri Lebesgue, Issue 1, 2018, Page(s) 87-125, ISSN 2644-9463
Publisher: Centre Mersenne
DOI: 10.5802/ahl.3

Spine representations for non-compact models of random geometry

Author(s): Jean-François Le Gall, Armand Riera
Published in: Probability Theory and Related Fields, Issue 181/1-3, 2021, Page(s) 571-645, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-021-01069-x

Geodesic stars in random geometry

Author(s): Jean-François Le Gall
Published in: The Annals of Probability, Issue 50/3, 2022, Page(s) 1013-1058, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-aop1553

Convergence of Eulerian triangulations

Author(s): Ariane Carrance
Published in: Electronic Journal of Probability, Issue 26/none, 2021, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-ejp579

On the minimal diameter of closed hyperbolic surfaces

Author(s): Thomas Budzinski, Nicolas Curien, Bram Petri
Published in: Duke Mathematical Journal, Issue 170/2, 2021, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.1215/00127094-2020-0083

The volume measure of the Brownian sphere is a Hausdorff measure

Author(s): Jean-François Le Gall
Published in: Electronic Journal of Probability, Issue 27, 2022, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-ejp837

Stable shredded spheres and causal random maps with large faces

Author(s): Jakob Björnberg, Nicolas Curien, Sigurdur Orn Stefansson
Published in: The Annals of Probability, Issue 50, 2022, Page(s) 2056-2084, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aop1579

First-passage percolation in random planar map and Tutte's bijection

Author(s): Thomas Lehéricy
Published in: Electronic Journal of Probability, Issue 27, 2022, Page(s) 1-50, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-ejp662