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math.PR2025★ 2 cited
First Passage percolation on a hyperbolic graph admits bi-infinite geodesics
Itai Benjamini, Romain Tessera
Given an infinite connected graph, a way to randomly perturb its metric is to assign random i.i.d. lengths to the edges. An open question attributed to Furstenberg is whether there…
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…