Noticias en español
Gagliardo-Nirenberg-Sobolev inequalities in domains
Abstract: Our objective is to estimate constants for a type of Gagliardo-Nirenberg-Sobolev inequalities in domains in euclidean space. We obtain a rough bound valid for bounded convex domains in dimension 3 and higher. When the domain is a cube, we obtain an improved bound in any dimension. In one dimension, the sharp constant is simply related to the sharp constant of the inequality on the real line and I will comment on the open question whether this holds true in higher dimensions.
Read MoreLinear inviscid damping and enhanced viscous dissipation of shear flows by the conjugate operator method
Abstract: We will show how we can use the classical Mourre commutator method to study the asymptotic behavior of the linearized incompressible Euler and Navier-Stokes at small viscosity equations about shear flows. We will focus on the case of the mixing layer. Joint work with E Grenier, T. Nguyen and A. Soffer
Read MoreIntertwinings and Stein’s factors for birth-death processes
Abstract: In this talk, I will present intertwinings between Markov processes and gradients, which are functional relations relative to the space-derivative of a Markov semigroup. I will recall the first-order relation , in the continuous case for diffusions and in the discrete case for birth-death processes, and introduce a new second-order relation for a discrete Laplacian. As the main application, new quantitative bounds on the Stein factors of discrete distributions are provided. Stein’s factors are a key component of Stein’s method, a collection of techniques to bound the distance...
Read MoreGagliardo-Nirenberg-Sobolev inequalities in domains
Abstract: Our objective is to estimate constants for a type of Gagliardo-Nirenberg-Sobolev inequalities in domains in euclidean space. We obtain a rough bound valid for bounded convex domains in dimension 3 and higher. When the domain is a cube, we obtain an improved bound in any dimension. In one dimension, the sharp constant is simply related to the sharp constant of the inequality on the real line and I will comment on the open question whether this holds true in higher dimensions. Joint work with Rafael Benguria and Cristobal Vallejos. ...
Read MoreOn the current-current correlation measure for random Schrödinger operators
Abstract: We review various properties of random Schrödinger operators and recall formulations of conductivity and current-current correlation measure. In this talk we will present a panoramic view and recent results on localized regime. We will focus in particular on the diagonal behaviour problem of the ccc-measure and explain how it is related to the localization length. This is a work in progress with J. Bellissard and G. De Nettis.
Read MoreAsymptotics for Optimal Transport between N-ples of points, with cost given by electrostatic interaction energy
Abstract: Consider the optimal transport problem N-ples of points, in which the transport cost between N points equals an electrostatic-type energy such as $\sum_{i\neq j} |x_i-x_j|^{-s}$ with $0<s<d$. We are led to a minimization problem for probability measures on $(\mathbb R^d)^N$, which is an N-marginal Optimal Transport problem, and has a direct physical interpretation. We prove the sharp large-N asymptotics for the above N-marginal transport problem at second order, namely beyond the mean-field continuum limit. To this aim we establish a general finite-range decomposition...
Read More