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The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process

Patrik L. Ferrari
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Abstract

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.

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Patrik L. Ferrari. 2007-01-08. The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process. https://arxiv.org/abs/math-ph/0701021

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