Related papers: Fisher Information and Logarithmic Sobolev Inequal…
In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously…
This short note investigates the compact embedding of degenerate matrix weighted Sobolev spaces into weighted Lebesgue spaces. The Sobolev spaces explored are defined as the abstract completion of Lipschitz functions in a bounded domain…
We introduce a concept of isoperimetric dimension for magnetic graphs, that is, graphs where every edge is assigned a complex number of modulus one. In analogy with the classical case, we show that isoperimetric inequalities imply Sobolev…
We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ…
In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost. This class of inequalities has been introduced in the recent…
Matrix concentration inequalities provide information about the probability that a random matrix is close to its expectation with respect to the $l_2$ operator norm. This paper uses semigroup methods to derive sharp nonlinear matrix…
Talagrand's inequality for independent Bernoulli random variables is extended to many interacting particle systems (IPS). The main assumption is that the IPS satisfies a log-Sobolev inequality. In this context it is also shown that a…
We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal…
A basilar property and a useful tool in the theory of Sobolev spaces is the density of smooth compactly supported functions in the space $W^{k,p}(\R^n)$ (i.e. the functions with weak derivatives of orders $0$ to $k$ in $L^p$). On Riemannian…
We prove an intrinsic Taylor-like formula for a class of Lie groups arising in the study of some sub-elliptic differential operators, namely the Kolmogorov operators. The estimate of the remainder is in terms of the intrinsic norm induced…
We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Pr\'ekopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $\dR^n$, with a strictly convex…
We study the connection between the $p$--Talagrand inequality and the $q$--logarithmic Sololev inequality for conjugate exponents $p\geq 2$, $q\leq 2$ in proper geodesic metric spaces. By means of a general Hamilton--Jacobi semigroup we…
In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a…
We prove Poincar\'e and Sobolev inequalities in matrix A${}_p$ weighted spaces. We then use these Poincar\'e inequalities to prove existence and regularity results for degenerate systems of elliptic equations whose degeneracy is governed by…
Building on Talagrand's proof of the Hoffmann-J{\o}rgensen inequality for $L_p$ spaces and its version for the exponential Orlicz spaces we provide a full characterization of Orlicz functions $\Psi$ for which an analogous inequality holds…
We prove concentration results for $\ell_p^n$ operator norms of rectangular random matrices and eigenvalues of self-adjoint random matrices. The random matrices we consider have bounded entries which are independent, up to a possible…
We prove that Sobolev spaces on Cartesian and warped products of metric spaces tensorize, only requiring that one of the factors is a doubling space supporting a Poincar\'e inequality.
The Heisenberg group is one of the simplest sub-Riemannian settings in which we can define non-elliptic H\"ormander type generators. We can then consider coercive inequalities associated to such generators. We prove that a certain class of…
We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are "balanced" between the density and log-density functions. The manifolds, $(\tilde{M}_{\lambda},\lambda\in…
Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fisher information in the Boolean Central Limit Theorem and…