TY - JOUR

T1 - Distribution of a Particle's Position in the ASEP with the Alternating Initial Condition

AU - Lee, Eunghyun

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

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U2 - 10.1007/s10955-010-0014-9

DO - 10.1007/s10955-010-0014-9

M3 - Article

AN - SCOPUS:77954862331

VL - 140

SP - 635

EP - 647

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 4

ER -