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

In this paper we will show how the results found in Cator and Pimentel 2009, 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.

preprint2010arXivOpen access
Eric CatorLeandro P. R. Pimentel
math-phmath.PRmath.MP
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Eric CatorLeandro P. R. Pimentel

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