2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172834In 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.13 pages, 4 figures, proceeding for the conference in honor of Percy Deift's 60th birthdayMathematical Physics82C22, 60K35, 15A52text