Thursday, May 22, 2025 - 11:30 in V2-210
Large-scale fluctuations for a diffusion in space-time random environment
A talk in the SPDEvent series by
Sotiris Kotitsas from University of Pisa
| Abstract: |
In this talk, we consider the following diffusion:
${\mathrm{d}}X_t = V(t, X_t){\mathrm{d}}t + \sqrt{\kappa} {\mathrm{d}}B_t,$
where $V$ is a random Gaussian field, white in time and smooth in space, and $(B_t)_{t\geq 0}$ is a $d$-dimensional Brownian motion. We are interested in the large-scale behaviour of the quenched density, $\theta(t, x)$, with respect to the Lebesgue measure. In $d = 1$, we will discuss known results about the model, and how it can be connected to the KPZ equation. In $d \geq 2$, we will discuss the model’s relevance to the statistical theory of turbulence. Finally, we will present ongoing work with Mario Maurelli and Dejun Luo about the fluctuations around the quenched local central limit theorem.
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