Uniqueness of the invariant measure for the phi42 dynamics in infinite volume (Benoit Dagallier, Imperial College London)

28.09.2026 16:15 – 18:00

I will report on a joint work with Roland Bauerschmidt and Hendrik Weber where we prove uniqueness of invariant measures of the phi42 dynamics in infinite volume, as soon as the susceptibility of the finite volume phi42 measure remains bounded. Invariant measures are known to be unique in finite volume and are given by the (finite volume) phi42 field theory. In infinite volume uniqueness may fail, for instance due to phase transitions.
Uniqueness is proven by adapting, to the field-theory setting, the Holley-Stroock-Zegarlinski approach to uniqueness for statistical mechanics models which I will present in detail. This approach is based on a volume-independent bound on the log-Sobolev constant of the associated dynamics, together with crude, model-independent bounds. In the phi42 case the bound on the log-Sobolev constant is known, but substantial work is needed to adapt the other parts of the argument.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Math Physics"

entrée libre