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Title:聽Busemann functions and Gibbs measures in directed polymer models on Z^2 .

Abstract: We consider the model of a nearest-neighbor random walk on the planar square lattice in a general iid space-time potential, which is also known as a directed polymer in a random environment. We prove results on existence, uniqueness (and non-uniqueness), and the law of large numbers for semi-infinite path measures. Our main tools are the Busemann functions, which are families of stochastic processes obtained through limits of ratios of partition functions.
Based on joint work with Firas Rassoul-Agha.