LARGE DEVIATIONS AND WANDERING EXPONENT FOR RANDOM WALK IN A DYNAMIC BETA ENVIRONMENT

• 成果类型: Article
• 署名作者: Balazs, Marton; Rassoul-Agha, Firas; Seppalainen, Timo
• 署名单位: University of Bristol; 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: 10.1214/18-AOP1306
• 发表日期: 2019
• 页码: 2186-2229
• 关键词: directed polymer; ratios

摘要

Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space and its marginal density function is a product of a beta density and a hypergeometric function. Under its averaged distribution, the transformed walk obeys the wandering exponent 2/3 that agrees with Kardar-Parisi-Zhang universality. The harmonic function in the Doob transform comes from a Busemann-type limit and appears as an extremal in a variational problem for the quenched large deviation rate function.