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Related papers: A Brascamp-Lieb type covariance estimate

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We prove that the best constant in the general Brascamp-Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear…

Classical Analysis and ODEs · Mathematics 2018-05-23 Jonathan Bennett , Neal Bez , Taryn C. Flock , Sanghyuk Lee

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,…

Functional Analysis · Mathematics 2009-07-17 F. Barthe , D. Cordero-Erausquin , M. Ledoux , B. Maurey

We give a $L^2\times L^2 \rightarrow L^2$ convolution estimate for singular measures supported on transversal hypersurfaces in $\mathbb{R}^n$, which improves earlier results of Bejenaru, Herr & Tataru as well as Bejenaru & Herr. The arising…

Classical Analysis and ODEs · Mathematics 2014-09-02 Herbert Koch , Stefan Steinerberger

Brascamp--Lieb-type, weighted Poincar\'{e}-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general $\kappa$-concave probability measures (in the hierarchy of convex measures). In analogy…

Probability · Mathematics 2009-06-10 Sergey G. Bobkov , Michel Ledoux

The Brascamp-Lieb inequality in harmonic analysis was proved by Brascamp and Lieb in the rank one case in 1976, and by Lieb in 1990. It says that in a certain inequality, the optimal constant can be determined by checking the inequality for…

Metric Geometry · Mathematics 2024-12-19 Károly J. Böröczky

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…

Econometrics · Economics 2024-02-27 Felix Chan , Laszlo Matyas

Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to…

High Energy Physics - Theory · Physics 2012-01-06 Axel Maas

We establish an effective upper bound for the Brascamp-Lieb constant associated to a weighted family of linear maps.

Classical Analysis and ODEs · Mathematics 2026-04-10 Timothée Bénard , Weikun He

The Borell-Brascamp-Lieb inequality is a classical extension of the Pr\'ekopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The stability of these inequalities has received significant…

Functional Analysis · Mathematics 2025-01-09 Alessio Figalli , Peter van Hintum , Marius Tiba

In the spirit of multi-scale modeling, we develop a theoretical framework for spin-lattice coupling that connects, on the one hand, to ab initio calculations of spin-lattice coupling parameters and, on the other hand, to the magneto-elastic…

In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…

Methodology · Statistics 2008-02-04 K. Triantafyllopoulos

We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extending previous results known for Gaussian measures. Actually, our result apply beyond the case…

Metric Geometry · Mathematics 2022-10-03 Dario Cordero-Erausquin , Liran Rotem

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

Machine Learning · Statistics 2021-02-03 Malik Tiomoko , Florent Bouchard , Guillaume Ginholac , Romain Couillet

We derive an improved Poincar\'e inequality in connection with the Babu\v{s}ka-Aziz and Friedrichs-Velte inequalities for differential forms by estimating the domain specific optimal constants figuring in the respective inequalities with…

Analysis of PDEs · Mathematics 2020-04-10 Sándor Zsuppán

We employ a Markov semigroup approach combined with the $\Gamma$-calculus to establish a generalized Beckner inequality associated with weighted Gaussian measures. As a direct consequence, we derive the corresponding Poincar\'e inequality…

Functional Analysis · Mathematics 2026-04-21 Nguyen Lam , Guozhen Lu , Andrey Russanov

We discuss theoretical and phenomenological aspects of the use of boson propagators with energy-dependent widths in predictions for high-energy scattering processes. In general, gauge invariance is violated in such calculations. We discuss…

We apply a new bosonization technique to relativistic field theories of fermions whose partition function is dominated by bosonic composites, and derive the effective action for these bosons. The derivation respects all symmetries,…

High Energy Physics - Lattice · Physics 2010-10-27 Sergio Caracciolo , Victor Laliena , Fabrizio Palumbo

A procedure to determine the initial ansatz for the co-frame and spin connection characterizing a Riemann-Cartan geometry respecting a given group of continuous symmetries is illustrated. Given a particular group of symmetries and assuming…

General Relativity and Quantum Cosmology · Physics 2026-05-13 R. J. van den Hoogen , H. Forance , L. Taylor , M. Lawton

A new proof is given for the fact that centered gaussian functions saturate the Euclidean forward-reverse Brascamp-Lieb inequalities, extending the Brascamp-Lieb and Barthe theorems. A duality principle for best constants is also developed,…

Functional Analysis · Mathematics 2019-08-30 Thomas A. Courtade , Jingbo Liu

We continue our investigation of the intertwining relations for Markov semigroups and extend the results of [9] to multi-dimensional diffusions. In particular these formulae entail new functional inequalities of Brascamp-Lieb type for…

Probability · Mathematics 2016-02-12 Marc Arnaudon , Michel Bonnefont , Aldéric Joulin