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 Raphaël Cerf.

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

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