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

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (33)

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, Issue 48/4, 2020, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-aop1406

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, Issue 47/6, 2019, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-aop1355

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, Issue 70/6, 2020, Page(s) 2425-2471, ISSN 0373-0956
Publisher: Association des Annales de I'Institut Fourier
DOI: 10.5802/aif.3369

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

infinite stable Boltzmann planar maps are subdiffusive

Author(s): Nicolas Curien, Cyril Marzouk
Published in: Probability and Mathematical Physics, Issue 2, 2021, Page(s) 1-26, ISSN 2690-1005
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/pmp.2021.2.1

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