Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials

2023/06/30 by Groathouse, Sean, Janjigian, Christopher, Rassoul-Agha, Firas · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.17714

Abstract

We establish the existence of generalized Busemann functions and Gibbs-Dobrushin-Landford-Ruelle measures for a general class of lattice random walks in random potential with finitely many admissible steps. This class encompasses directed polymers in random environments, first- and last-passage percolation, and elliptic random walks in both static and dynamic random environments in all dimensions and with minimal assumptions on the random potential.

Cited by

• Strong existence and uniqueness of the tilt-indexed Busemann process in the planar corner growth model
• Permutation invariance in last-passage percolation and the distribution of the Busemann process

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