Busemann functions and the speed of a second class particle in the rarefaction fan
Probability
2010-08-12 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1008.1812,
title = {Busemann functions and the speed of a second class particle in the rarefaction fan},
author = {Eric Cator and Leandro P. R. Pimentel},
journal= {arXiv preprint arXiv:1008.1812},
year = {2010}
}