2008/04/25 by Craig A. Tracy, Harold Widom · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60K35
paper · pdf · doi:10.1007/s10955-008-9562-7
published as Journal of Statistical Physics 132 (2008), 291-300. · 12 Pages. Version 3 includes a scaling conjecture
arxiv created 2008/04/25 · openalex publication_date 2008/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In previous work the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers, and consider the distribution function for the m'th particle from the left. In the previous work an infinite series of multiple integrals was derived for this distribution. In this note we show that the series can be summed to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive (non-rigorously, at this writing) a scaling limit.