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

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

2011-10-17

arxiv.org/abs/1110.3544v2

Mathematics

Probability

33 pages, 3 figures. One figure added to the previous version, two more remarks added, typos fixed

Scientific paper

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.

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