How fast does the range of simple random walk grow?

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Itaï Benjamini, Justin Salez
DOI: 10.48550/arxiv.2602.11051
Cited by: 0

Abstract

Consider a discrete-time simple random walk $(X_t)_{t\ge 0}$ on an infinite, connected, locally finite simple graph $G$, and let \[ R_t := |\{X_0,\ldots,X_t\}| \] denote its range. The main result of this revised note is that positive vertex isoperimetry already forces linear expected range, with no bounded-degree assumption: if \[ ι_V(G) := \inf_{0

Fields of Study & Subjects

Stochastic processes and statistical mechanics Geometric Analysis and Curvature Flows Mathematical Dynamics and Fractals

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 February 2026
Language
EN
Document type
Preprint