Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
By Shiri Artstein-Avidan, Bo'az Klartag, Carsten Schütt, Elisabeth M. Werner. 2011
75 citations recorded by the source corpus.
Abstract We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincare inequality for the Gaussian measure.
Subfields: Applied Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/2ca380f36b6b9f2554cc6509e846eb054de6d3fe
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In Applied Mathematics
- Umut Caglar
- Rafael Villa
- David Alonso-Guti'errez
- Bernardo González Merino
- C. Hugo Jiménez
- Elisabeth M. Werner
- Deping Ye
- Monika Ludwig
In Statistics and Probability
Citations in the corpus
- Rogers–Shephard inequality for log-concave functions (2014, background): “This has generated an increasing interest to extend several important parameters of convex bodies to functional parameters [5,6,10,12,19,22,24] in the class of log-concave functions.”
- Functional Versions of Lp-Affine Surface Area and Entropy Inequalities (2014, unknown): “The characterization of equality in the reverse log-Sobolev inequality of [4] had remained open in [4].”
- Divergence for s-concave and log concave functions (2013, methodology): “The proof, which we include for completeness, follows [6].”