Behavior of the Poincaré constant along the Polchinski renormalization flow
Résumé
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.
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