Upcoming Talks

Ista white

On the two-dimensional KPZ and Stochastic Heat Equation

VIENNA PROBABILITY SEMINAR

Date
Tuesday, December 15, 2020 16:30 - 17:15
Speaker
Francesco Caravenna (Università degli Studi di Milano-Bicocca)
Location
Online via Zoom
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Contact

We consider the Kardar-Parisi-Zhang equation (KPZ) and the multiplicative Stochastic Heat Equation (SHE) in two space dimensions, driven by with space-time white noise. These PDEs are very singular and lack a solution theory, so it is standard to introduce a regularization - e.g. by convolving the noise with a smooth mollifier - and to investigate the behavior of the solutions when the regularization is removed. Interestingly, these regularized solutions are closely linked to a much studied model in statistical mechanics, the so-called directed polymer in random environment. Building on this link, we show that a phase transition emerges, as the noise strength is varied on a logarithmic scale. In the sub-critical regime, the solutions of the regularized KPZ and SHE (suitably centered and rescaled) converge to an explicit Gaussian field, the solution of an *additive* Stochastic Heat Equation. We finally discuss the critical regime, where many questions are open. Based on joint works with Rongfeng Sun and Nikos Zygouras


Qr image
Download ICS Download invitation
Back to eventlist