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math.PR2025
Spread-out percolation on transitive graphs of polynomial growth
Panagiotis Spanos, Matthew Tointon
Let be a vertex-transitive graph of superlinear polynomial growth. Given , let be the graph on the same vertex set as , with two vertices joined by an edge if and…
math.PR2024
Sharp relations between volume growth, isoperimetry and escape probability in vertex-transitive graphs
Romain Tessera, Matthew Tointon
We prove sharp bounds on the probability that the simple random walk on a vertex-transitive graph escapes the ball of radius before returning to its starting point. In particul…