Title: Weak universality of the KPZ equation

Speaker: Martin Hairer

Date: August 12
Time: 8:30 - 9:30
Room: Ballroom C

Chair: John Ball

Abstract: The KPZ equation is a popular model of one-dimensional interface propagation. From heuristic consideration, it is expected to be "universal" in the sense that any "weakly asymmetric" or "weakly noisy" microscopic model of interface propagation should converge to it if one sends the asymmetry (resp. noise) to zero and simultaneously looks at the interface at a suitable large scale. In particular, although the equation is not even classically well-posed, any "reasonable" numerical method is expected to converge to it, possibly with limiting parameters different from the "naive" ones. However, the only microscopic models for which this has been proven so far all exhibit some very particular structure allow to perform a microscopic equivalent to the Hopf-Cole transform. In this talk, we will see that there exists a rather large class of continuous models of interface propagation for which convergence to KPZ can be proven rigorously. The main tool for both the proof of convergence and the identification of the limit is the recently developed theory of regularity structures, but with an interesting twist.


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