Large Deviations for the height function of the deformed polynuclear growth.

Mucciconi Matteo, University of Warwick

The deformed polynuclear growth is a growth process that generalizes the polynuclear growth studied in the context of KPZ universality class. In this talk, I will discuss the mathematical derivation of large time large deviations for the height function. Rare events, as functions of the time t, display distinct decay rates based on whether the height function grows significantly larger (upper tail) or smaller (lower tail) than the expected value. Upper tails exhibit an exponential decay with rate function which we determine explicitly. Conversely, the lower tails experience a more rapid decay and the rate function is given in terms of a variational problem. Our analysis relies on two inputs. The first is a connection between the height function hand an important measure on the set of integer partitions, the Poissonized Plancherel measure, which stems from nontrivial applications of the celebrated Robinson-Schensted-Knuth correspondence. The second ingredient is the derivation of a priori convexity bounds for the rate function, which combines combinatorial and probabilistic arguments. This is a joint work with S.Das (Chicago) and Y.Liao (Wisconsin-Madison).

Area: IS1 - A promenade through integrable system (Alessandra Occelli)

Keywords: Large Deviations, Kardar Parisi Zhang universality class, convexity