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Session S04 - Random Walks and Related Topics

Friday, July 16, 14:20 ~ 14:50 UTC-3

The parabolic Anderson model on a Galton-Watson tree

Renato Soares dos Santos

UFMG, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider the non-negative solution to the parabolic Anderson model (i.e., the heat equation with random multiplicative potential) on a supercritical Galton-Watson tree with bounded degrees. The potential is taken i.i.d. with double-exponential upper tails. We obtain second-order asymptotics of the rescaled total mass of the solution in terms of a variational formula. Analysis of the variational formula under further assumptions suggests mass concentration in subtrees with minimal degrees.

Joint work with Frank den Hollander (Leiden University) and Wolfgang König (TU Berlin, WIAS Berlin).

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