LARGE DEVIATION RATE FUNCTIONS FOR THE PARTITION FUNCTION IN A LOG-GAMMA DISTRIBUTED RANDOM POTENTIAL

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...

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Bibliographic Details
Published in:The Annals of probability 2013-11, Vol.41 (6), p.4248-4286
Main Authors: Georgiou, Nicos, Seppäläinen, Timo
Format: Article
Language:English
Subjects:
60F10
60K35
60K37
Convexity
Coordinate systems
Dimensional analysis
Directed polymer in random environment
Free energy
Integers
large deviations
Lattice theory
Mathematical functions
Mathematical inequalities
Mathematical lattices
Mathematical problems
Mathematics
partition function
Polymers
Probability distribution
Random variables
random walk in random potential
Rectangles
Studies
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Summary: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.
ISSN:0091-1798
2168-894X
DOI:10.1214/12-aop768