Behavior of the Poincar{é} constant along the Polchinski renormalization flow

We control the behavior of the Poincar{é} constant along the Polchinski renormalization flow using a dynamic version of $Γ$-calculus. We also treat the case of higher order eigenvalues. 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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