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

Gérard Ben Arous, Manuel Cabezas, Alexander Fribergh

Research output: Contribution to journalArticlepeer-review


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
Issue number1-2
StatePublished - Jun 1 2019


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

ASJC Scopus subject areas

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


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