One more proof of the Alexandrov-Fenchel inequality
We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.
math.MG↗
arXiv subjects
D. Cordero-Erausquin
Publications and source records attributed to D. Cordero-Erausquin.
Invariances in variance estimates
We provide variants and improvements of the Brascamp-Lieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log-concave measures with many symmetries and to non-interacting conservative spin systems.
math.FA↗
Hypercontractive measures, Talagrand's inequality, and influences
We survey several Talagrand type inequalities and their application to influences with the tool of hypercontractivity for both discrete and continuous, and product and non-product models. The approach covers similarly by a simple interpolation the framework of geometric influences recently developed by N. Keller, E. Mossel and A. Sen. Geometric Brascamp-Lieb decompositions are also considered in this context.
math.PR↗
Correlation and Brascamp-Lieb inequalities for Markov semigroups
This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres and symmetric groups). Our aim is twofold. Firstly, we provide a general, unifying, framework based on Markov generators, in order to cover a variety of examples of interest going beyond previous investigations. Secondly, we put forward the combinatorial reasons for which unexpected exponents occur in these inequalities.
math.FA↗