Lipschitz-continuity of time constant in generalized First-passage percolation

Van Hao Can, Shuta Nakajima and Van Quyet Nguyen

Stochastic Processes and their Applications, 2024, vol. 175, issue C

Abstract: In this article, we consider a generalized First-passage percolation model, where each edge in Zd is independently assigned an infinite weight with probability 1−p, and a random finite weight otherwise. The existence and positivity of the time constant have been established in Cerf and Théret (2016). Recently, using sophisticated multi-scale renormalizations, Cerf and Dembin (2022) proved that the time constant of chemical distance in super-critical percolation is Lipschitz continuous. In this work, we propose a different approach leveraging lattice animal theory and a simple one-step renormalization with the aid of Russo’s formula, to show the Lipschitz continuity of the time constant in generalized First-passage percolation.

Date: 2024
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DOI: 10.1016/j.spa.2024.104402

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