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Collision probabilities in the rarefaction fan of asymmetric exclusion processes
Ferrari, Pablo A.; Martin, James B.; Gonçalves, PatríciaWe consider the one-dimensional asymmetric simple exclusion process (asep) in which particles jump to the right at rate p 2 (1/2, 1] and to the left at rate 1 − p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occuppied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converg...
Second and third class particles in TASEP
Gonçalves, Patrícia; Ferrari, Pablo A.; Martin, JamesWe consider the nearest neighbors one-dimensional totally asymmetric simple exclusion process starting with ones to the left of the origin, a second class particle at the origin, a third class particle at site 1 and no particles to the right of site 1. We show that the probability that the third class particle is to the right of the second class particle at time $t$ converges to $2/3$ as $t\to\infty$....
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