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

Gerard Ben Arous, Manuel Cabezas, Alexander Fribergh

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)553-646
Number of pages94
JournalProbability Theory and Related Fields
Volume174
Issue number1-2
DOIs
StatePublished - Jun 1 2019

Fingerprint

Brownian Excursion
Branching Random Walk
Simple Random Walk
Scaling Limit
Rescaling
Brownian motion
High-dimensional
Trace
Converge
Random walk
Ants
Scaling
Integrated

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Scaling limit for the ant in a simple high-dimensional labyrinth. / Ben Arous, Gerard; Cabezas, Manuel; Fribergh, Alexander.

In: Probability Theory and Related Fields, Vol. 174, No. 1-2, 01.06.2019, p. 553-646.

Research output: Contribution to journalArticle

Ben Arous, Gerard ; Cabezas, Manuel ; Fribergh, Alexander. / Scaling limit for the ant in a simple high-dimensional labyrinth. In: Probability Theory and Related Fields. 2019 ; Vol. 174, No. 1-2. pp. 553-646.
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