Gaussian free field on the tree subject to a hard wall constraint (Lisa Hartung, Johannes Gutenberg University Mainz)

07.04.2025 16:15 – 18:00

Abstract:
We consider the Gaussian free field on a binary tree (also known as branching random walk) under the constraint that the values at all leaves at generation n are non-negative. We obtain a remarkably precise description of the conditional law and the conditional field. The conditioning leads to an upward shift of the whole field. We obtain sharp estimates on this upward shift (up to o(1) terms). We show that the properly rescaled maximum converges to a Gumbel distribution (without a random shift!), and the rescaled minimum is exponentially distributed. We use tools from DGFFs on general graphs and estimates on random walks that are weakly attracted to zero either through a pinning potential or a drift. The talk is based on joint work with M. Fels (Technion) and O. Louidor (Technion).

Lieu

Conseil Général 7-9, Room 1-15, Séminaire Math Physics

entrée libre