Absence of weak disorder for directed polymers on supercritical percolation clusters

Abstract

We study the directed polymer model on infinite clusters of supercritical Bernoulli percolation containing the origin in dimensions $d\ge 3$, and prove that for almost every realization of the cluster and every strictly positive value of the inverse temperature, the polymer is in a strong disorder phase, answering a question from Cosco, Seroussi, and Zeitouni, see arXiv:2010.09503.

19 pages, 1 figure, this version appeared in the Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

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