### Stationary measures in the Kardar-Parisi-Zhang universality class

Mathematical Physics Seminar

27th October 2023, 1:45 pm – 3:30 pm

Fry Building, 2.04

The Kardar-Parisi-Zhang (KPZ) equation is a non-linear stochastic partial differential equation. It was introduced in Physics in 1986, as a toy model to describe the stochastic growth of interfaces -- modelling for instance propagation of the front of a bacterial colony -- which feature universal scaling exponents and statistics. It is now related to many other physical phenomena exhibiting out of equilibrium fluctuations.

The study of the KPZ equation and its universality class started in the mathematics community around 2000 when it was discovered that, surprisingly, the fluctuations in the KPZ class are the same as those of eigenvalues of random matrices. The theory is now very rich and related to various other areas such as algebraic combinatorics, integrable systems or stochastic PDEs.

In this talk, I will first review a few emblematic mathematical results about the KPZ universality class. Then I will report on recent progress about stationary measures of the KPZ equation (and other models) on bounded domains.

*Biography:*

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/ca606a8996ed46b19147bedee93a721d1d

*Organiser*: Thomas Bothner

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