A new Universality Class in (1+1)-dimensions: the Brownian Castle

22.09.2020 15:00 - 15:50

Giuseppe Cannizzaro (University of Warwick)

Abstract: In the context of randomly fluctuating interfaces in (1+1)-dimensions two Universality Classes have generally been considered, the Kardar-Parisi-Zhang and the Edwards-Wilkinson. Models within these classes exhibit universal fluctuations under 1:2:3 and 1:2:4 scaling respectively.

Starting from a "infinite-temperature" version of the classical Ballistic Deposition model we will show that this picture is not exhaustive and another Universality Class, whose scaling exponents are 1:1:2, has to be taken into account. We will describe how it arises, briefly discuss its connections to KPZ and introduce a new stochastic process, the Brownian Castle, deeply connected to the Brownian Web, which should capture the large-scale behaviour of models within this Class. This talk is based on a joint ongoing work with Martin Hairer.

M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Online via Zoom