Prof. Dr. Martin Hairer, University of Warwick, Vortrag: Solving the KPZ equation
Thursday, 25.10.2012 16:30 im Raum M5
Abstract: The KPZ equation was introduced in the eighties as a model of surface growth,
but it was soon realised that its solution is a much more "universal" object
describing the crossover between the Gaussian universality class and the KPZ
universality class. The mathematical proof of its universality however is still an
open problem, in particular because of the lack of a good approximation theory
for the equation.
In this talk, we present a new, robust, notion of solution to the KPZ equation.
Our approach allows to factor the solution map into a "universal" (i.e. independent
of initial condition) measurable map, composed with an "abstract" solution map
with very good continuity properties. This lays the foundations for a robust
approximation theory to the KPZ equation, which is needed to prove its universality.
As a byproduct of the construction, we obtain very detailed regularity estimates
on the solutions, as well as a new homogenisation result.