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Ratios of partition functions for the log-gamma polymer
Version 2 2023-06-12, 06:37
Version 1 2023-06-09, 00:08
journal contribution
posted on 2023-06-12, 06:37 authored by Nicos GeorgiouNicos Georgiou, Firas Rassoul-Agha, Timo Seppalainen, Atilla YilmazWe 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.
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Publication status
- Published
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- Published version
Journal
Annals of ProbabilityISSN
0091-1798Publisher
Institute of Mathematical Statistics (IMS)External DOI
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5Volume
43Page range
2282-2331Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2016-01-26First Open Access (FOA) Date
2016-01-26First Compliant Deposit (FCD) Date
2016-01-26Usage metrics
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