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

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arxiv 2306.17714 v2 pith:ST2IG4LG submitted 2023-06-30 math.PR

Sean Groathouse , Christopher Janjigian , Firas Rassoul-Agha This is my paper · ORCID
classification math.PR
keywords randomwalksbusemannclassenvironmentsexistencefunctionsgeneralized
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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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  1. Permutation invariance in last-passage percolation and the distribution of the Busemann process

    math.PR 2025-06 conditional novelty 8.0 of 10

    The joint law of Busemann increments in i.i.d. exponential LPP is exactly represented by last-passage increments on a finite grid with inhomogeneous exponential weights.

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