INFINITE STABLE BOLTZMANN PLANAR MAPS ARE SUBDIFFUSIVE

Nicolas Curien; Cyril Marzouk

doi:10.2140/pmp.2021.2.1

INFINITE STABLE BOLTZMANN PLANAR MAPS ARE SUBDIFFUSIVE

Nicolas Curien
, Cyril Marzouk

Université Paris-Saclay

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

The infinite discrete stable Boltzmann maps are generalisations of the well-known uniform infinite planar quadrangulation in the case where large degree faces are allowed. We show that the simple random walk on these random lattices is always subdiffusive with exponent less than¹. Our method is based on 3 stationarity and geometric estimates obtained via the peeling process which are of individual interest.

langue originale	Anglais
Pages (de - à)	1-26
Nombre de pages	26
journal	Probability and Mathematical Physics
Volume	2
Numéro de publication	1
Les DOIs	https://doi.org/10.2140/pmp.2021.2.1
état	Publié - 1 janv. 2021

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10.2140/pmp.2021.2.1

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title = "INFINITE STABLE BOLTZMANN PLANAR MAPS ARE SUBDIFFUSIVE",

abstract = "The infinite discrete stable Boltzmann maps are generalisations of the well-known uniform infinite planar quadrangulation in the case where large degree faces are allowed. We show that the simple random walk on these random lattices is always subdiffusive with exponent less than1. Our method is based on 3 stationarity and geometric estimates obtained via the peeling process which are of individual interest.",

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author = "Nicolas Curien and Cyril Marzouk",

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N2 - The infinite discrete stable Boltzmann maps are generalisations of the well-known uniform infinite planar quadrangulation in the case where large degree faces are allowed. We show that the simple random walk on these random lattices is always subdiffusive with exponent less than1. Our method is based on 3 stationarity and geometric estimates obtained via the peeling process which are of individual interest.

AB - The infinite discrete stable Boltzmann maps are generalisations of the well-known uniform infinite planar quadrangulation in the case where large degree faces are allowed. We show that the simple random walk on these random lattices is always subdiffusive with exponent less than1. Our method is based on 3 stationarity and geometric estimates obtained via the peeling process which are of individual interest.

KW - anomalous diffusion

KW - peeling

KW - random maps

KW - random walk

KW - subdiffusivity

U2 - 10.2140/pmp.2021.2.1

DO - 10.2140/pmp.2021.2.1

M3 - Article

AN - SCOPUS:85168088781

SN - 2690-0998

VL - 2

SP - 1

EP - 26

JO - Probability and Mathematical Physics

JF - Probability and Mathematical Physics

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INFINITE STABLE BOLTZMANN PLANAR MAPS ARE SUBDIFFUSIVE

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