Remarks on Gaussian Noise Stability, Brascamp-Lieb and Slepian Inequalities
نویسندگان
چکیده
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 Gaussian measure.
منابع مشابه
Information-Theoretic Perspectives on Brascamp-Lieb Inequality and Its Reverse
We introduce an inequality which may be viewed as a generalization of both the Brascamp-Lieb inequality and its reverse (Barthe’s inequality), and prove its information-theoretic (i.e. entropic) formulation. This result leads to a unified approach to functional inequalities such as the variational formula of Rényi entropy, hypercontractivity and its reverse, strong data processing inequalities,...
متن کاملThe Brascamp–lieb Inequalities: Finiteness, Structure and Extremals
We consider the Brascamp–Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of centred gaussian extremals. For arbitrary extremals we completely address the issue of existence, and partly address the issue of uniqueness. We also analyse th...
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 کاملSum 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 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 کامل