The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
数学物理
2008-11-01 v1 math.MP
摘要
In the totally asymmetric simple exclusion process (TASEP) two processes arise in the large time limit: the Airy_1 and Airy_2 processes. The Airy_2 process is an universal limit process occurring also in other models: in a stochastic growth model on 1+1-dimensions, 2d last passage percolation, equilibrium crystals, and in random matrix diffusion. The Airy_1 and Airy_2 processes are defined and discussed in the context of the TASEP. We also explain a geometric representation of the TASEP from which the connection to growth models and directed last passage percolation is immediate.
引用
@article{arxiv.math-ph/0701021,
title = {The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process},
author = {Patrik L. Ferrari},
journal= {arXiv preprint arXiv:math-ph/0701021},
year = {2008}
}
备注
13 pages, 4 figures, proceeding for the conference in honor of Percy Deift's 60th birthday