Expected hitting time estimates on finite graphs

Laurent Saloff-Coste and Yuwen Wang

Stochastic Processes and their Applications, 2025, vol. 185, issue C

Abstract: The expected hitting time from vertex a to vertex b, H(a,b), is the expected value of the time it takes a random walk starting at a to reach b. In this paper, we give estimates for H(a,b) when the distance between a and b is comparable to the diameter of the graph, and the graph satisfies a Harnack condition. We show that, in such cases, H(a,b) can be estimated in terms of the volumes of balls around b. Using our results, we estimate H(a,b) on various graphs, such as rectangular tori, some convex traces in Zd, and fractal graphs. Our proofs use heat kernel estimates.

Keywords: Hitting time; Random walks; Green’s function; Heat kernel estimates (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104626

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