KPZ-TYPE FLUCTUATION EXPONENTS FOR INTERACTING DIFFUSIONS IN EQUILIBRIUM

• 成果类型: Article
• 署名作者: Landon, Benjamin; Noack, Christian; Sosoe, Philippe
• 署名单位: University of Toronto; Purdue University System; Purdue University; Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1617
• 发表日期: 2023
• 页码: 1139-1191
• 关键词: dimensional directed polymer; corner growth-model; Brownian motions; Scaling Limit; equation; bounds

摘要

We consider systems of N diffusions in equilibrium interacting through a potential V. We study a height function, which, for the special choice V (x) = e(-x), coincides with the partition function of a stationary semidis-crete polymer, also known as the (stationary) O'Connell-Yor polymer. For a general class of smooth convex potentials (generalizing the O'Connell-Yor case), we obtain the order of fluctuations of the height function by proving matching upper , lower bounds for the variance of order N-2/3, the ex-pected scaling for models lying in the KPZ universality class. The models we study are not expected to be integrable , our methods are analytic and nonperturbative, making no use of explicit formulas or any results for the O'Connell-Yor polymer.