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

Eunghyun Lee

doi:10.1007/s10955-010-0014-9

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

Eunghyun Lee

University of California at Davis

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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(X_m(t)≤x) where X_m(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(X_m(t)≤x) to a determinantal form together with an extra product.

Original language	English
Pages (from-to)	635-647
Number of pages	13
Journal	Journal of Statistical Physics
Volume	140
Issue number	4
DOIs	https://doi.org/10.1007/s10955-010-0014-9
Publication status	Published - 2010
Externally published	Yes

Funding

This work was supported in part by National Science Foundation through the grant DMS-0906387.

Keywords

ASEP
Bethe Ansatz
TASEP

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-010-0014-9

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title = "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 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.",

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N1 - Funding Information: This work was supported in part by National Science Foundation through the grant DMS-0906387.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - ASEP

KW - Bethe Ansatz

KW - TASEP

UR - https://www.scopus.com/pages/publications/77954862331

UR - https://www.scopus.com/pages/publications/77954862331#tab=citedBy

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M3 - Article

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SN - 0022-4715

VL - 140

SP - 635

EP - 647

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 4

ER -

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

Abstract

Funding

Keywords

ASJC Scopus subject areas

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