The 2d random heat equation and the 2d KPZ equation with a general Gaussian noise


Event details

Date 14.06.2024
Hour 10:00
Speaker Sotiris Kotitsas (Warwick)
Category Conferences - Seminars
Event Language English

We consider the stochastic heat equation

and the related KPZ equation

in the critical dimension d = 2 where V is a Gaussian random potential and β is the noise strength. We will focus on the case where the potential is not white in time and study the large-scale fluctuations of u(t, x) and h(t, x). We show that after renormalizing, the fluctuations converge to the Edwards-Wilkinson limit with an explicit effective variance and constant effective diffusivity. We discuss our main tools, a specific Markov chain on the space of paths and an extension of the Kallianpur-Robbins law to a specific regenerative process. Time permitting, we will also discuss possible future directions.

Practical information

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Probability and stochastic analysis Seminar