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Crossing probabilities in asymmetric exclusion processes | | Pablo A. Ferrari
; Patricia Goncalves
; James B. Martin
; | | Date: |
10 Apr 2008 | | Abstract: | We 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 | | Services: | Forum | Review | PDF | Favorites | |
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