Abstract
We control the behavior of the Poincaré constant along the Polchinski renormalization flow using a dynamic version of [Formula: see text]-calculus. We also treat the case of higher order eigenvalues. Our method generalizes a method introduced by Klartag and Putterman to analyze the evolution of log-concave distributions along the heat flow. Furthermore, we apply it to general [Formula: see text]-measures and discuss the interpretation in terms of transport maps.
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