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

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

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.

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Probability and Mathematical Physics
Volume	2
Issue number	1
DOIs	https://doi.org/10.2140/pmp.2021.2.1
Publication status	Published - 1 Jan 2021

Keywords

anomalous diffusion
peeling
random maps
random walk
subdiffusivity

Access to Document

10.2140/pmp.2021.2.1

Cite this

@article{3428910f386b49738416b1717150abc1,

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.",

keywords = "anomalous diffusion, peeling, random maps, random walk, subdiffusivity",

author = "Nicolas Curien and Cyril Marzouk",

year = "2021",

month = jan,

day = "1",

doi = "10.2140/pmp.2021.2.1",

language = "English",

volume = "2",

pages = "1--26",

journal = "Probability and Mathematical Physics",

issn = "2690-0998",

number = "1",

}

TY - JOUR

T1 - INFINITE STABLE BOLTZMANN PLANAR MAPS ARE SUBDIFFUSIVE

AU - Curien, Nicolas

AU - Marzouk, Cyril

PY - 2021/1/1

Y1 - 2021/1/1

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

IS - 1

ER -

INFINITE STABLE BOLTZMANN PLANAR MAPS ARE SUBDIFFUSIVE

Abstract

Keywords

Access to Document

Fingerprint

Cite this