Kurt Johansson:The two-time distribution in local random growth

Abstract: There has recently been much interest in local random growth models belonging to the so called
Kardar-Parisi-Zhang universality class named after the Stochastic PDE with the same name. We are interested in the
local random growth of a one-dimensional interface. In certain integrable cases much can be said about the fluctuations
of the interface and I will review some of the relevant background.
This provides the background to a recent result of mine on the so called two-time distribution in these models. More specifically
I work with something called the the zero temperature Brownian semi-discrete directed polymer.
This two-time distribution should be the universal two-time distribution in many models e.g. last-passage percolation and 
related random growth models. The resulting formula and its derivation is very complicated and I will only be able to
give some hints. The ultimate goal is to understand also multi-time distributions. In a combinatorial language this can be thought
of as understanding the random surface defined by Viennot's shadowing construction for a random permutation.