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

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

2010-08-10

arxiv.org/abs/1008.1812v1

Mathematics

Probability

Scientific paper

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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