Distribution of a particle's position in the ASEP with the {alternating} initial condition

Abstract

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

Version 3 expands the introduction and adds more references. Published version

References in corpus (4)

• Fluctuation properties of the TASEP with periodic initial configuration
• A Fredholm Determinant Representation in ASEP
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• On ASEP with Step Bernoulli Initial Condition

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• Current moments of 1D ASEP by duality
• A Pfaffian representation for flat ASEP
• Exact formulas for random growth with half-flat initial data
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• The current distribution of the multiparticle hopping asymmetric diffusion model
• On ASEP with Periodic Step Bernoulli Initial Condition
• Distribution of a second-class particle's position in the two-species ASEP with a special initial configuration