Francesco Caravenna (University of Milano-Bicocca)

will speak on

On the two-dimensional KPZ and Stochastic Heat Equation

Time: 3:00PM
Date: Wed 11th November 2020
Location: Online [map]

Abstract: We consider the Kardar-Parisi-Zhang equation (KPZ) and the multiplicative Stochastic Heat Equation (SHE) in two space dimensions, driven by space-time white noise. These singular PDEs are 'critical' and lack a solution theory, so it is standard to consider regularized versions of these equations - e.g. by convolving the noise with a smooth mollifier - and to investigate the behavior of the solutions when the regularization is removed.

Based on joint works with Rongfeng Sun and Nikos Zygouras, we show that these regularized solutions undergo a phase transition as the noise strength is varied on a logarithmic scale. In the sub-critical regime, the regularized solutions of both KPZ and SHE exhibit so-called Edwards-Wilkinson fluctuations, i.e. they converge (after centering and rescaling) to the solution of the *additive* Stochastic Heat Equation, with a renormalized noise strength. We finally discuss the critical regime, where many questions are open.

Zoom Link:
https://ucd-ie.zoom.us/j/83491228915?pwd=WWV3ZkNGNzVXdGxLRlR0dkdMYUtMZz09

Meeting ID: 834 9122 8915
Passcode: 698437

(This talk is part of the Probability series.)

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