# Fluctuations of the log-gamma polymer free energy with general parameters and slopes

@article{Barraquand2021FluctuationsOT,
title={Fluctuations of the log-gamma polymer free energy with general parameters and slopes},
author={Guillaume Barraquand and Ivan Corwin and Evgeni Dimitrov},
journal={Probability Theory and Related Fields},
year={2021}
}
• Published 22 December 2020
• Mathematics
• Probability Theory and Related Fields
We prove that the free energy of the log-gamma polymer between lattice points (1, 1) and (M,N) converges to the GUE Tracy-Widom distribution in the M1/3 scaling, provided that N/M remains bounded away from zero and infinity. We prove this result for the model with inverse gamma weights of any shape parameter θ > 0 and furthermore establish a moderate deviation estimate for the upper tail of the free energy in this case. Finally, we consider a non i.i.d. setting where the weights on finitely…
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