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

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 .

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Bibliographic Details
Published in:Probability theory and related fields 2019-06, Vol.174 (1-2), p.553-646
Main Authors: Ben Arous, Gérard, Cabezas, Manuel, Fribergh, Alexander
Format: Article
Language:English
Subjects:
Brownian motion
Economics
Finance
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Random walk
Random walk theory
Rescaling
Statistics for Business
Theoretical
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Description
Summary: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 .
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-018-0876-3