Competition interfaces and second class particles

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dc.creatorFerrari, Pablo A.
dc.creatorPimentel, Leandro P. R.
dc.date2004-06-16
dc.date2005-08-25
dc.date.accessioned2026-07-07T05:09:19Z
dc.date.available2026-07-07T05:09:19Z
dc.descriptionThe one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z^2. We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an asymptotic random direction. As a consequence we get a new proof for the strong law of large numbers for the second class particle in the rarefaction fan and describe the distribution of the asymptotic angle of the competition interface.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117905000000080 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0406333
dc.identifierhttp://arxiv.org/abs/math/0406333
dc.identifierAnnals of Probability 2005, Vol. 33, No. 4, 1235-1254
dc.identifierdoi:10.1214/009117905000000080
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71585
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35 (Primary) 82B. (Secondary)
dc.titleCompetition interfaces and second class particles
dc.typetext

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