Abstract
The free-energy fluctuations of the discrete directed polymer in $1+1$ dimensions is conjecturally in the Tracy–Widom universality class at all finite temperatures and in the intermediate disorder regime. Seppäläinen’s log-gamma polymer was proven to have GUE Tracy–Widom fluctuations in a restricted temperature range by Borodin, Corwin and Remenik [Comm. Math. Phys. 324 (2013) 215–232]. We remove this restriction, and extend this result into the intermediate disorder regime. This result also identifies the scale of fluctuations of the log-gamma polymer in the intermediate disorder regime, and thus verifies a conjecture of Alberts, Khanin and Quastel [Ann. Probab. 42 (2014) 1212–1256]. Using a perturbation argument, we show that any polymer that matches a certain number of moments with the log-gamma polymer also has Tracy–Widom fluctuations in intermediate disorder.
Citation
Arjun Krishnan. Jeremy Quastel. "Tracy–Widom fluctuations for perturbations of the log-gamma polymer in intermediate disorder." Ann. Appl. Probab. 28 (6) 3736 - 3764, December 2018. https://doi.org/10.1214/18-AAP1404
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