NONINTERSECTING RANDOM WALKS IN THE NEIGHBORHOOD OF A SYMMETRIC TACNODE

• 成果类型: Article
• 署名作者: Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre
• 署名单位: Brandeis University; University of Bonn
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP726
• 发表日期: 2013
• 页码: 2599-2647
• 关键词: polynuclear growth-model; dynamical correlations; spacing distributions; plancherel measures; Brownian motions; schur process; pearcey; fluctuations; UNIVERSALITY; EIGENVALUE

摘要

Consider a continuous time random walk in Z with independent and exponentially distributed jumps +/- 1. The model in this paper consists in an infinite number of such random walks starting from the complement of {-m, -m + 1, ... , m - 1, m} at time -t, returning to the same starting positions at time t, and conditioned not to intersect. This yields a determinantal process, whose gap probabilities are given by the Fredholm determinant of a kernel. Thus this model consists of two groups of random walks, which are contained within two ellipses which, with the choice m similar or equal to 2t to leading order, just touch: so we have a tacnode. We determine the new limit extended kernel under the scaling m = left perpendicular2t +sigma t(1/3)right perpendicular, where parameter sigma controls the strength of interaction between the two groups of random walkers.