Directed polymers on supercritical percolation clusters
In this talk, we introduce a model of directed polymers on infinite clusters of supercritical Bernoulli percolation containing the origin in dimensions d ≥ 3. We 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. The proof is based on a utilization of a fractional moment calculation, as well as a large deviation-type estimate on the number of effectively one-dimensional tubes present in the intersection of a large box and the supercritical cluster.
Area: IS12 - Random surfaces (Alessandra Cipriani)
Keywords: Bernoulli percolation, directed polymers, supercritical regime
Il paper è coperto da copyright.