Ratios of partition functions for the log-gamma polymer

Georgiou, Nicos, Rassoul-Agha, Firas, Seppalainen, Timo and Yilmaz, Atilla (2015) Ratios of partition functions for the log-gamma polymer. Annals of Probability, 43 (5). pp. 2282-2331. ISSN 0091-1798

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Abstract

We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition in- terface of percolation and arises as the limit of quenched polymer measures. We prove this limit for the exactly solvable log-gamma polymer, as a consequence of almost sure limits of ratios of parti- tion functions. These limits of ratios give the Busemann functions of the log-gamma polymer, and furnish centered cocycles that solve a variational formula for the limiting free energy. Limits of ratios of point-to-point and point-to-line partition functions manifest a duality between tilt and velocity that comes from quenched large deviations under polymer measures. In the log-gamma case, we identify a fam- ily of ergodic invariant distributions for the random walk in random environment.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Nicos Georgiou
Date Deposited: 26 Jan 2016 13:50
Last Modified: 07 Mar 2017 04:41
URI: http://sro.sussex.ac.uk/id/eprint/59424

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