Correlation and Brascamp-Lieb inequalities for Markov semigroups
نویسنده
چکیده
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.
منابع مشابه
Sum of Square Proof for Brascamp-Lieb Type Inequality
Brascamp-Lieb inequalities [5] is an important mathematical tool in analysis, geometry and information theory. There are various ways to prove Brascamp-Lieb inequality such as heat flow method [4], Brownian motion [11] and subadditivity of the entropy [6]. While Brascamp-Lieb inequality is originally stated in Euclidean Space, [8] discussed Brascamp-Lieb inequality for discrete Abelian group an...
متن کاملGlobal Nonlinear Brascamp–lieb Inequalities
We prove global versions of certain known nonlinear Brascamp– Lieb inequalities under a natural homogeneity assumption. We also establish a conditional theorem allowing one to generally pass from local to global nonlinear Brascamp–Lieb estimates under such a homogeneity assumption.
متن کاملRemarks on Gaussian Noise Stability, Brascamp-Lieb and Slepian Inequalities
E. Mossel and J. Neeman recently provided a heat flow monotonicity proof of Borell’s noise stability theorem. In this note, we develop the argument to include in a common framework noise stability, Brascamp-Lieb inequalities (including hypercontractivity), and even a weak form of Slepian inequalities. The scheme applies furthermore to families of measures with are more log-concave than the Gaus...
متن کاملBrascamp-Lieb Inequalities for Non-Commutative Integration
We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings. 2000 Mathematics Subject Classification: 47C15, 15A45, 26D15
متن کاملFinite Bounds for Hölder-brascamp-lieb Multilinear Inequalities
A criterion is established for the validity of multilinear inequalities of a class considered by Brascamp and Lieb, generalizing well-known inequalties of Rogers and Hölder, Young, and Loomis-Whitney. 1. Formulation Consider multilinear functionals (1.1) Λ(f1, f2, · · · , fm) = ∫
متن کامل