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The free-energy fluctuations of the discrete directed polymer in 1+1dimensions is conjecturally in the Tracy-Widom universality class at all finitetemperatures and in the intermediate disorder regime. Sepp\"al\"ainen'slog-gamma polymer was proven to have GUE Tracy-Widom fluctuations in arestricted temperature range by Borodin et. al. (2013). We remove thisrestriction, and extend this result into the intermediate disorder regime. Thisresult also identifies the scale of fluctuations of the log-gamma polymer inthe intermediate disorder regime, and thus verifies a conjecture of Alberts et.al. (2010). Using a perturbation argument, we show that any polymer thatmatches a certain number of moments with the log-gamma polymer also hasTracy-Widom fluctuations in intermediate disorder.

Tracy-Widom fluctuations for perturbations of the log-gamma polymer in intermediate disorder