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arXiv · 1008.1812

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

Eric Cator·Leandro P. R. Pimentel
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Abstract

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.

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Eric Cator, Leandro P. R. Pimentel. 2010-08-10. Busemann functions and the speed of a second class particle in the rarefaction fan. https://arxiv.org/abs/1008.1812

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