Mustazee Rahman: On shocks in the TASEP

Abstract: The TASEP particle system runs into traffic jams when the initial particle density increases in the direction of flow. It servers as a microscopic model of shocks in Burgers' equation. I will describe work with Jeremy Quastel on a specialization of TASEP, where we identify limiting joint fluctuations of particles at the shock by using determinantal formulae for its correlation functions. The limit is described in terms of random matrix laws.