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Ratios of partition functions for the log-gamma polymer

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Version 2 2023-06-12, 06:37
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journal contribution
posted on 2023-06-12, 06:37 authored by Nicos GeorgiouNicos Georgiou, Firas Rassoul-Agha, Timo Seppalainen, Atilla Yilmaz
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Annals of Probability

ISSN

0091-1798

Publisher

Institute of Mathematical Statistics (IMS)

Issue

5

Volume

43

Page range

2282-2331

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-01-26

First Open Access (FOA) Date

2016-01-26

First Compliant Deposit (FCD) Date

2016-01-26

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