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

• 成果类型: Article
• 署名作者: Georgiou, Nicos; Seppaelaeinen, Timo
• 署名单位: Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP768
• 发表日期: 2013
• 页码: 4248-4286
• 关键词: directed polymers; increasing subsequences; random environment; diffusion

摘要

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.