Many interesting stochastic PDEs arising from statistical physics are ill-posed in the sense that they involve products between distributions, so the solutions to these equations are obtained after renormalisations, which typically change the original equation by a quantity that is infinity. I will use KPZ and Phi^4_3 as two examples to explain the meanings of these infinities. As a consequence, we will see how these two equations, interpreted after suitable renormalisations, arise naturally as universal limits for two distinct classes of systems. Part of the talk based on joint works with Martin Hairer, Cyril Labbe and Hao Shen.
Biography
Weijun Xu is a postdoc researcher at the University of Warwick. He obtained his Ph.D. from Oxford. His research interests include stochastic PDEs, probability, and rough paths.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai