The KPZ equation is a popular model of one-dimensional in-

terface 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. The only microscopic models for which

this has been proven so far all exhibit very particular that allow to perform

a microscopic equivalent to the Cole-Hopf transform. The main bottleneck

for generalisations to larger classes of models was that until recently it was

not even clear what it actually means to solve the equation, other than via

the Cole-Hopf transform. In this talk, we will see that there exists a rather

large class of continuous models of interface propagation for which conver-

gence to KPZ can be proven rigorously. The main tool for both the proof

of convergence and the identication of the limit is the recently developed

theory of regularity structures, but with an interesting twist.

When? | 03.06.2015 16:00 |
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Where? | PER 08 Phys 2.52 Chemin du Musée 3 1700 Fribourg |

Contact | Department of Mathematics isabella.schmutz@unifr.ch |