CONVERGENCE DE CARTES NON - BIPARTIES VIA LA SYMÉTRISATION D’ARBRES ÉTIQUETÉS

Louigi A Ddario-Be R R Y; Marie Albenque

doi:10.5802/ahl.84

CONVERGENCE DE CARTES NON - BIPARTIES VIA LA SYMÉTRISATION D’ARBRES ÉTIQUETÉS

Louigi A Ddario-Be R R Y
, Marie Albenque

École Polytechnique

McGill University

Research output: Contribution to journal › Article › peer-review

Abstract

— Fix an odd integer p ≥ 5. Let M_n be a uniform p-angulation with n vertices, endowed with the uniform probability measure on its vertices. We prove that there exists C_p ∈ R₊ such that, after rescaling distances by C_p/n^1/4, M_n converges in distribution for the Gromov–Hausdorff–Prokhorov topology towards the Brownian map. To prove the pre-ceding fact, we introduce a bootstrapping principle for distributional convergence of random labelled plane trees. In particular, the latter allows to obtain an invariance principle for labeled multitype Galton–Watson trees, with only a weak assumption on the centering of label displacements.

Translated title of the contribution	CONVERGENCE OF NON - BIPARTITE MAPS VIA SYMMETRIZATION OF LABELEDTREES
Original language	English
Pages (from-to)	653-683
Number of pages	31
Journal	Annales Henri Lebesgue
Volume	4
DOIs	https://doi.org/10.5802/ahl.84
Publication status	Published - 1 Jan 2021

Keywords

Brownian map
Brownian snake
Invariance principle
Random planar maps
Random trees

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title = "CONVERGENCE DE CARTES NON - BIPARTIES VIA LA SYM{\'E}TRISATION D{\textquoteright}ARBRES {\'E}TIQUET{\'E}S",

abstract = "— Fix an odd integer p ≥ 5. Let Mn be a uniform p-angulation with n vertices, endowed with the uniform probability measure on its vertices. We prove that there exists Cp ∈ R+ such that, after rescaling distances by Cp/n1/4, Mn converges in distribution for the Gromov–Hausdorff–Prokhorov topology towards the Brownian map. To prove the pre-ceding fact, we introduce a bootstrapping principle for distributional convergence of random labelled plane trees. In particular, the latter allows to obtain an invariance principle for labeled multitype Galton–Watson trees, with only a weak assumption on the centering of label displacements.",

keywords = "Brownian map, Brownian snake, Invariance principle, Random planar maps, Random trees",

author = "\{A Ddario-Be R R Y\}, Louigi and Marie Albenque",

year = "2021",

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doi = "10.5802/ahl.84",

language = "English",

volume = "4",

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journal = "Annales Henri Lebesgue",

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T1 - CONVERGENCE DE CARTES NON - BIPARTIES VIA LA SYMÉTRISATION D’ARBRES ÉTIQUETÉS

AU - A Ddario-Be R R Y, Louigi

AU - Albenque, Marie

PY - 2021/1/1

Y1 - 2021/1/1

N2 - — Fix an odd integer p ≥ 5. Let Mn be a uniform p-angulation with n vertices, endowed with the uniform probability measure on its vertices. We prove that there exists Cp ∈ R+ such that, after rescaling distances by Cp/n1/4, Mn converges in distribution for the Gromov–Hausdorff–Prokhorov topology towards the Brownian map. To prove the pre-ceding fact, we introduce a bootstrapping principle for distributional convergence of random labelled plane trees. In particular, the latter allows to obtain an invariance principle for labeled multitype Galton–Watson trees, with only a weak assumption on the centering of label displacements.

AB - — Fix an odd integer p ≥ 5. Let Mn be a uniform p-angulation with n vertices, endowed with the uniform probability measure on its vertices. We prove that there exists Cp ∈ R+ such that, after rescaling distances by Cp/n1/4, Mn converges in distribution for the Gromov–Hausdorff–Prokhorov topology towards the Brownian map. To prove the pre-ceding fact, we introduce a bootstrapping principle for distributional convergence of random labelled plane trees. In particular, the latter allows to obtain an invariance principle for labeled multitype Galton–Watson trees, with only a weak assumption on the centering of label displacements.

KW - Brownian map

KW - Brownian snake

KW - Invariance principle

KW - Random planar maps

KW - Random trees

UR - https://www.scopus.com/pages/publications/86000738149

U2 - 10.5802/ahl.84

DO - 10.5802/ahl.84

M3 - Article

AN - SCOPUS:86000738149

SN - 2644-9463

VL - 4

SP - 653

EP - 683

JO - Annales Henri Lebesgue

JF - Annales Henri Lebesgue

ER -

CONVERGENCE DE CARTES NON - BIPARTIES VIA LA SYMÉTRISATION D’ARBRES ÉTIQUETÉS

Abstract

Keywords

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