Asymptotics in ASEP with Step Initial Condition |
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Authors: | Craig A Tracy and Harold Widom |
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Institution: | (1) Department of Mathematics, University of California, Davis, CA 95616, USA;(2) Department of Mathematics, University of California, Santa Cruz, CA 95064, USA |
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Abstract: | In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step
initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for
the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use
this formula to obtain three asymptotic results for the positions of these particles. In one an apparently new distribution
function arises and in another the distribution function F
2 arises. The latter extends a result of Johansson on TASEP to ASEP, and hence proves KPZ universality for ASEP with step initial
condition. |
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Keywords: | |
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