Behavior of the Poincaré constant along the Polchinski renormalization flow

Jordan Serres (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We control the behavior of the Poincaré constant along the Polchinski renormalization flow using a dynamic version of Γ-calculus. Our method generalizes a method introduced by B. Klartag and E. Putterman to analyze the evolution of log-concave distributions along the heat flow. Furthermore, we apply it to general ϕ 4-measures and discuss the interpretation in terms of transport maps.

Domaines: Probabilités [math.PR]; Théorie spectrale [math.SP]; Analyse fonctionnelle [math.FA]

Jordan Serres. Behavior of the Poincaré constant along the Polchinski renormalization flow. 2022. ⟨hal-03740297v1⟩