The local time of a random walk on growing hypercubes

2009/03/16 by Pierre Andreoletti, Andreoletti, Pierre
Computer Science · Mathematics · Physics and Astronomy · #60G50 #60J55 #Complex Network Analysis Techniques #FOS: Mathematics #Interconnection Networks and Systems #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0903.2696

openalex publication_date 2009/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a random walk in a random environment (RWRE) on \Z^d, 1 ≤ d < +∞. The main assumptions are that conditionned on the environment the random walk is reversible. Moreover we construct our environment in such a way that the walk can't be trapped on a single point like in some particular RWRE but in some specific d-1 surfaces. These surfaces are basic surfaces with deterministic geometry. We prove that the local time in the neighborhood of these surfaces is driven by a function of the (random) reversible measure. As an application we get the limit law of the local time as a process on these surfaces.

Citations

• Limit law of the local time for Brox's diffusion

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