HIGH TEMPERATURE LIMITS FOR (1+1)-DIMENSIONAL DIRECTED POLYMER WITH HEAVY-TAILED DISORDER

• 成果类型: Article
• 署名作者: Dey, Partha S.; Zygouras, Nikos
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1067
• 发表日期: 2016
• 页码: 4006-4048
• 关键词: free-energy

摘要

The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel [Ann. Probab. 42 (2014) 1212-1256]. It was proved that at inverse temperature beta n(-gamma) with gamma = 1/4 the partition function, centered appropriately, converges in distribution and the limit is given in terms of the solution of the stochastic heat equation. This result was obtained under the assumption that the disorder variables posses exponential moments, but its universality was also conjectured under the assumption of six moments. We show that this conjecture is valid and we further extend it by exhibiting classes of different universal limiting behaviors in the case of less than six moments. We also explain the behavior of the scaling exponent for the log-partition function under different moment assumptions and values of gamma.