May 29, 2023 to June 2, 2023
Paul Sabatier University, Toulouse
Europe/Paris timezone

Piettro Caputo: Subadditivity and factorization of the relative entropy in spin systems and random permutations

Jun 2, 2023, 9:45 AM
Paul Sabatier University, Toulouse

Paul Sabatier University, Toulouse

Institut de Mathématiques de Toulouse 118, route de Narbonne - Bat. 1R3 F-31062 Toulouse Cedex 9


Pietro Caputo


We discuss some recent developments in the analysis of subadditivity and factorization properties of the relative entropy for spin systems on arbitrary graphs, and for uniformly random permutations. For spin systems these imply optimal modified log-Sobolev inequality for arbitrary block dynamics in the uniqueness region, including the case of non-local evolutions such as the Swendsen-Wang dynamics. For random permutations, an application our bounds proves a long standing conjecture on the permanent of any matrix with nonnegative entries.

Presentation materials