Fluctuations in random surface growth

VIENNA PROBABILITY SEMINAR

The physical phenomenon of random surface growth can be captured by stochastic models which belong to the Kardar-Parisi-Zhang (KPZ) universality class. In the talk we introduce a typical example, the totally asymmetric simple exclusion process (TASEP). Its limiting fluctuations are known to be related to random matrix theory. We mention a few further related models in the universality class. Then we explain some details about the recent work with Patrik Ferrari about the upper tail decay of the limiting fluctuations of TASEP with random initial condition. The problem is related to the maximum of a Brownian motion with parabolic drift.