Large deviation rate functions for the partition function in a log-gamma distributed random potential

Abstract

We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the $1+1$-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dimensions.

Published in at http://dx.doi.org/10.1214/12-AOP768 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Cited by in corpus (16)

• Ratios of partition functions for the log-gamma polymer
• Half-space Macdonald processes
• Localization Transition for Polymers in Poissonian Medium
• Fluctuations of the log-gamma polymer free energy with general parameters and slopes
• Large deviations of the free energy in the O'Connell-Yor polymer
• Large deviations for some corner growth models with inhomogeneity
• Upper tail bounds for stationary KPZ models
• Stationary measures for two dual families of finite and zero temperature models of directed polymers on the square lattice
• Upper tail large deviations in Brownian directed percolation
• Analytical Methods and Field Theory for Disordered Systems
• Large deviations for the $q$-deformed polynuclear growth
• High moments of the SHE in the clustering regimes
• Quenched Point-to-Point Free Energy for Random Walks in Random Potentials
• Variational formulas and cocycle solutions for directed polymer and percolation models
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models
• Free energy of directed polymers in random environment in $1+1$-dimension at high temperature