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.