Collision probabilities in the rarefaction fan of asymmetric exclusion processes


Autoria(s): FERRARI, Pablo A.; GONCALVES, Patricia; MARTIN, James B.
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

19/04/2012

19/04/2012

2009

Resumo

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (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 occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

CNPq

FAPESP

FAPESP Brasil[06/58527-0]

Identificador

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, v.45, n.4, p.1048-1064, 2009

0246-0203

http://producao.usp.br/handle/BDPI/16664

10.1214/08-AIHP303

http://dx.doi.org/10.1214/08-AIHP303

Idioma(s)

eng

Publicador

INST MATHEMATICAL STATISTICS

Relação

Annales de l Institut Henri Poincare-probabilites Et Statistiques

Direitos

openAccess

Copyright INST MATHEMATICAL STATISTICS

Palavras-Chave #Asymmetric simple exclusion process #Rarefaction fan #Second-class particle #Growth model #COMPETITION INTERFACES #PARTICLES #PROFILE #Statistics & Probability
Tipo

article

original article

publishedVersion