Random Walks on Graphs with Regular Volume Growth
T. Coulhon1998, Geometric And Functional Analysis
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Abstract
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This paper addresses properties of nearest neighbourhood random walks on infinite graphs with a focus on upper bounds of transition probabilities. The authors establish that under specific assumptions on the graph structure and transition probability, the upper bound can be represented as a function of the volume of balls in the graph and an exponential decay related to the combinatorial distance. The results draw parallels with known estimates in the context of Brownian motion on Riemannian manifolds, indicating that the study of random walks can reveal broader geometric and analytic properties of infinite graphs.
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