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

• Nicos Georgiou ^[1] ; Timo Seppäläinen ^[2]
  1. [1] University of Utah

     University of Utah

     Estados Unidos

     
  2. [2] University of Wisconsin–Madison

     University of Wisconsin–Madison

     City of Madison, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 6, 2013, págs. 4248-4286
• Idioma: inglés
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• Resumen

  • 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.