Annals of Probability

Busemann functions and the speed of a second class particle in the rarefaction fan

Eric Cator and Leandro P. R. Pimentel

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In this paper we will show how the results found in [Probab. Theory Related Fields 154 (2012) 89–125], about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan, in either the totally asymetric exclusion process or the Hammersley interacting particle process. The method will be to use the well-known last-passage percolation description of the exclusion process and of the Hammersley process, and then the well-known connection between second class particles and competition interfaces.

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Ann. Probab., Volume 41, Number 4 (2013), 2401-2425.

First available in Project Euclid: 3 July 2013

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C21: Dynamic continuum models (systems of particles, etc.)

TASEP second class particles rarefaction fan


Cator, Eric; Pimentel, Leandro P. R. Busemann functions and the speed of a second class particle in the rarefaction fan. Ann. Probab. 41 (2013), no. 4, 2401--2425. doi:10.1214/11-AOP709.

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