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

Sean Groathouse; Christopher Janjigian; Firas Rassoul-Agha

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arXiv · 2306.17714

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

Sean Groathouse·Christopher Janjigian·Firas Rassoul-Agha

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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.

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Sean Groathouse, Christopher Janjigian, Firas Rassoul-Agha. 2023-06-30. Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials. https://arxiv.org/abs/2306.17714

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