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arXiv · 2208.08186

Behavior of the Poincar{\'e} constant along the Polchinski renormalization flow

Jordan Serres
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Abstract

We control the behavior of the Poincar{\'e} constant along the Polchinski renormalization flow using a dynamic version of $\Gamma$-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 $\Phi$ 4-measures and discuss the interpretation in terms of transport maps.

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Jordan Serres. 2022-08-17. Behavior of the Poincar{\'e} constant along the Polchinski renormalization flow. https://arxiv.org/abs/2208.08186

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