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We control the behavior of the Poincar{\'e} constant along the Polchinski renormalization flow using a dynamic version of $\Gamma$-calculus.
Renormalization and effective Lagrangians
Joseph Polchinski · 1984
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Sur les inégalités de Sobolev logarithmiques
Cécile Ané, Sébastien Blachère, Djalil Chafaï, Pierre Fougères, Ivan Gentil, Florent Malrieu, Cyril Roberto, and Grégory Scheffer · 2000
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Some applications of mass transport to Gaussian-type inequalities
Dario Cordero-Erausquin · 2002
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Entropy jumps in the presence of a spectral gap
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Dan Mikulincer and Yair Shenfeld · 2021
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