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.
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This work was supported in part by National Science Foundation through the grant DMS-0906387.
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Lee, E. Distribution of a Particle’s Position in the ASEP with the Alternating Initial Condition. J Stat Phys 140, 635–647 (2010). https://doi.org/10.1007/s10955-010-0014-9
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DOI: https://doi.org/10.1007/s10955-010-0014-9