Dyson Ferrari-Spohn diffusions and ordered walks under area tilts

• 成果类型: Article
• 署名作者: Ioffe, Dmitry; Velenik, Yvan; Wachtel, Vitali
• 署名单位: Technion Israel Institute of Technology; University of Geneva; University of Augsburg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0751-z
• 发表日期: 2018
• 页码: 11-47
• 关键词: entropic repulsion; brownian-motion

摘要

We consider families of non-colliding random walks above a hard wall, which are subject to a self-potential of tilted area type. We view such ensembles as effective models for the level lines of a class of -dimensional discrete-height random surfaces in statistical mechanics. We prove that, under rather general assumptions on the step distribution and on the self-potential, such walks converge, under appropriate rescaling, to non-intersecting Ferrari-Spohn diffusions associated with limiting Sturm-Liouville operators. In particular, the limiting invariant measures are given by the squares of the corresponding Slater determinants.