Relation between the geometry of sign clusters of the 2D GFF and its Wick powers (Titus Lupu, Sorbonne Université)

07.10.2024 16:15 – 18:00

Abstract:
In 1990, Le Gall showed an asymptotic expansion of the epsilon-neighborhood of a planar Brownian trajectory (Wiener sausage) into powers of 1/|log eps|, that involves the renormalized self-intersection local times. In my talk I will present an analogue of this in the case of the 2D GFF. In the latter case, there is an asymptotic expansion of the epsilon-neighborhood of a sign cluster of the 2D GFF into half-integer powers of 1/|log eps|, with the coefficients of the expansion being related to the renormalized (Wick) powers of the GFF.

Lieu

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

entrée libre