Construction of Gibbs measures for quartic interactions.

par Nikolay Tzvetkov (UMPA ÉNS Lyon)

mardi 30 sept. 2025, 10:15 → 11:15 Europe/Paris

Fokko (ICJ)

 In 3d we will consider a free energy associated with a fractional Laplacian in the presence of a quartic interaction. We will show that there is a minimal power of the fractional Laplacian which makes that the Gibbs measure is absolutely continuous with respect to the underlying Gaussian measure. In 4d we will construct a non trivial radial Gibbs measure. This is in sharp contrast with the non radial situation in which a triviality result is known.