B. Dembin: The time constant for Bernoulli percolation is Lipschitz continuous strictly above pc

Abstract: We consider the standard model of i.i.d. first passage percolation on \mathbb Z^d given a distribution G on [0,+\infty] (+\infty is allowed). When G([0,+\infty])p_c(d). In this case, the travel time between two points is equal to the length of the shortest path between the two points in a bond percolation of parameter p. We show that the function p\mapsto \mu_{G_p} is Lipschitz continuous on every interval [p_0,1], where p_0>p_c(d).

This is a joint work with Raphaƫl Cerf.


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