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01 October 2020
 
  » arxiv » 0804.1770

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Crossing probabilities in asymmetric exclusion processes
Pablo A. Ferrari ; Patricia Goncalves ; James B. Martin ;
Date 10 Apr 2008
AbstractWe consider the one-dimensional asymmetric simple exclusion process in which particles jump to the right at rate p and to the left at rate 1-p, interacting by exclusion. Suppose that the initial state has first-class particles to the left of the origin, a second-class particle at the origin, a third-class particle at site 1 and holes to the right of site 1. We show that the probability that the second-class particle overtakes the third-class particle is (1+p)/3p. We obtain various limiting results about the joint behavior of the second-class and third-class particles, and a partial extension to a system with a further (fourth-class) particle.
Source arXiv, 0804.1770
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