Scaling limit for the ant in a simple high-dimensional labyrinth

Gérard Ben Arous; Manuel Cabezas; Alexander Fribergh

doi:10.1007/s00440-018-0876-3

Scaling limit for the ant in a simple high-dimensional labyrinth

Gérard Ben Arous, Manuel Cabezas, Alexander Fribergh

Mathematics

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

Abstract

We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk in Z ^d converges to the Brownian motion on the integrated super-Brownian excursion when d> 14.

Original language	English (US)
Pages (from-to)	553-646
Number of pages	94
Journal	Probability Theory and Related Fields
Volume	174
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-018-0876-3
State	Published - Jun 1 2019

Keywords

Branching random walk
Random environments
Random walk
Spatial tree
Super-process

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1007/s00440-018-0876-3

Cite this

@article{be5992ff7da34002a703c1adffddb939,

title = "Scaling limit for the ant in a simple high-dimensional labyrinth",

abstract = " We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk in Z d converges to the Brownian motion on the integrated super-Brownian excursion when d> 14. ",

keywords = "Branching random walk, Random environments, Random walk, Spatial tree, Super-process",

author = "{Ben Arous}, G{\'e}rard and Manuel Cabezas and Alexander Fribergh",

note = "Funding Information: The authors would like to thank the referees whose work helped significantly improved the article. Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2019",

month = jun,

day = "1",

doi = "10.1007/s00440-018-0876-3",

language = "English (US)",

volume = "174",

pages = "553--646",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Scaling limit for the ant in a simple high-dimensional labyrinth

AU - Ben Arous, Gérard

AU - Cabezas, Manuel

AU - Fribergh, Alexander

N1 - Funding Information: The authors would like to thank the referees whose work helped significantly improved the article. Publisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk in Z d converges to the Brownian motion on the integrated super-Brownian excursion when d> 14.

AB - We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk in Z d converges to the Brownian motion on the integrated super-Brownian excursion when d> 14.

KW - Branching random walk

KW - Random environments

KW - Random walk

KW - Spatial tree

KW - Super-process

UR - http://www.scopus.com/inward/record.url?scp=85065317466&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065317466&partnerID=8YFLogxK

U2 - 10.1007/s00440-018-0876-3

DO - 10.1007/s00440-018-0876-3

M3 - Article

AN - SCOPUS:85065317466

SN - 0178-8051

VL - 174

SP - 553

EP - 646

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -

Scaling limit for the ant in a simple high-dimensional labyrinth

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this