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March 2020 Busemann functions and Gibbs measures in directed polymer models on $\mathbb{Z}^{2}$
Christopher Janjigian, Firas Rassoul-Agha
Ann. Probab. 48(2): 778-816 (March 2020). DOI: 10.1214/19-AOP1375

Abstract

We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles and use them to prove new results on existence, uniqueness/nonuniqueness, and asymptotic directions of semi-infinite polymer measures (solutions to the Dobrushin–Lanford–Ruelle equations). We also prove nonexistence of covariant or deterministically directed bi-infinite polymer measures. Along the way, we prove almost sure existence of Busemann function limits in directions where the limiting free energy has some regularity.

Citation

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Christopher Janjigian. Firas Rassoul-Agha. "Busemann functions and Gibbs measures in directed polymer models on $\mathbb{Z}^{2}$." Ann. Probab. 48 (2) 778 - 816, March 2020. https://doi.org/10.1214/19-AOP1375

Information

Received: 1 October 2018; Revised: 1 March 2019; Published: March 2020
First available in Project Euclid: 22 April 2020

zbMATH: 07199862
MathSciNet: MR4089495
Digital Object Identifier: 10.1214/19-AOP1375

Subjects:
Primary: 60K35, 60K37

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 2 • March 2020
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