Probability and Statistics seminar – Probability and Statistics seminar

Thursday 10.09.2026, 13h30, room MNO 1.010
Fabrice Baudoin (Aarhus University), Moment Estimates and Intermittency for the Stochastic Heat Equation on Fractals
Abstract: We study the parabolic Anderson model, or stochastic heat equation with multiplicative space-time white noise, on bounded fractal spaces, with particular emphasis on the Sierpiński gasket equipped with the Kigami Laplacian and Dirichlet boundary conditions. A central question is how the geometry of the underlying space influences the large-time behavior of the solution. Using heat kernel estimates, Wiener chaos expansions, and hypercontractivity, we derive upper bounds for the growth of moments of the solution and obtain matching lower bounds in the second moment. These estimates quantify the competition between the dissipativity of the Dirichlet heat semigroup and the excitability induced by the multiplicative noise. They also provide evidence for intermittency phenomena on fractals, where high peaks of the solution carry most of the mass at large times. The results reveal the role of the Hausdorff and walk dimensions in determining the Lyapunov-type exponents governing moment growth.

Probability & Statistics Seminar