Open Access
July 2013 Busemann functions and the speed of a second class particle in the rarefaction fan
Eric Cator, Leandro P. R. Pimentel
Ann. Probab. 41(4): 2401-2425 (July 2013). DOI: 10.1214/11-AOP709


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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Eric Cator. Leandro P. R. Pimentel. "Busemann functions and the speed of a second class particle in the rarefaction fan." Ann. Probab. 41 (4) 2401 - 2425, July 2013.


Published: July 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1276.60108
MathSciNet: MR3112921
Digital Object Identifier: 10.1214/11-AOP709

Primary: 60K35 , 82C21

Keywords: Rarefaction fan , second class particles , TASEP

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 4 • July 2013
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