Distribution of a Particle's Position in the ASEP with the Alternating Initial Condition

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Abstract

In this paper we give the distribution of the position of a particle in the asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is, we find P(Xm(t)≤x) where Xm(t) is the position of the particle at time t which was at m=2k-1, k∈ Z at t=0. As in the ASEP with step initial condition, there arises a new combinatorial identity for the alternating initial condition, and this identity relates the integrand of the integral formula for P(Xm(t)≤x) to a determinantal form together with an extra product.

Original languageEnglish
Pages (from-to)635-647
Number of pages13
JournalJournal of Statistical Physics
Volume140
Issue number4
DOIs
Publication statusPublished - 2010

Keywords

  • ASEP
  • Bethe Ansatz
  • TASEP

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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