WIAS Preprint No. 1205, (2007)

The universal Airy$_1$ and Airy$_2$ processes in the totally asymmetric simple exclusion process


  • Ferrari, Patrik

2010 Mathematics Subject Classification

  • 82C22 60K35 15A52


  • Simple exclusion process, universality, Airy process, random matrices


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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