Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials
Probability
2025-01-16 v2
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.
Keywords
Cite
@article{arxiv.2306.17714,
title = {Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials},
author = {Sean Groathouse and Christopher Janjigian and Firas Rassoul-Agha},
journal= {arXiv preprint arXiv:2306.17714},
year = {2025}
}
Comments
58 pages, 4 figures. Reorganized for better exposition. Added more examples and discussion