Related papers: A sharp commutator estimate for all Riesz modulate…

On a smooth compact connected $d$-dimensional Riemannian manifold $M$, if $0 < s < d$ then an asymptotically equidistributed sequence of finite subsets of $M$ that is also well-separated yields a sequence of Riesz $s$-energies that…

We present a variant of Mourre's commutator theory. We apply it to prove the limiting absorption principle for Schr\"odinger operators with a perturbed Wigner-Von Neumann potential at suitable energies. To our knowledge, this result is new…

We explore the finite bias DC differential conductance of a correlated quantum dot under the influence of an AC field, from the low-temperature Kondo to the finite temperature Coulomb blockade regime. Real-time simulations are performed…

In this paper, we study optimal estimates and comparison of the coefficients in the Gegenbauer series expansion. We propose an alternative derivation of the contour integral representation of the Gegenbauer expansion coefficients which was…

We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent samples from an absolutely continuous distribution on…

Let $(M^\circ, g)$ be an asymptotically conic manifold, in the sense that $M^\circ$ compactifies to a manifold with boundary $M$ in such a way that $g$ becomes a scattering metric on $M$. A special case of particular interest is that of…

We present an optimal transport framework for performing regression when both the covariate and the response are probability distributions on a compact Euclidean subset $\Omega\subset\mathbb{R}^d$, where $d>1$. Extending beyond compactly…

In the first part of the paper we consider accelerated first order optimization method for convex functions with $L$-Lipschitz-continuous gradient, that is able to automatically adapts to problems which satisfies Polyak-{\L}ojasiewicz…

We study mixed weak type inequalities for the commutator $[b,T]$, where $b$ is a BMO function and $T$ is a Calder\'on-Zygmund operator. More precisely, we prove that for every $t>0$ \begin{equation*}%\label{tesis_teo2.2} uv(\{x\in\R^n:…

In this paper we establish an optimal Lorentz space estimate for the Riesz potential acting on curl-free vectors: There is a constant $C=C(\alpha,d)>0$ such that \[ \|I_\alpha F \|_{L^{d/(d-\alpha),1}(\mathbb{R}^d;\mathbb{R}^d)} \leq C…

We study the one-dimensional discrete Schr\"odinger operator with the skew-shift potential $2\lambda\cos\left(2\pi \left(\binom{j}{2} \omega+jy+x\right)\right)$. This potential is long conjectured to behave like a random one, i.e., it is…

We propose new weak error bounds and expansion in dimension one for optimal quantization-based cubature formula for different classes of functions, such that piecewise affine functions, Lipschitz convex functions or differentiable function…

We extend the recent boost operator formalism for relativistic Compton scattering calculations to also account for polarization. This allows us to provide general, exact expressions for the polarized Sunyaev-Zeldovich (SZ) effect sourced…

Let $(W,H,\mu)$ be the classical Wiener space on $\R^d$. Assume that $X=(X_t(x))$ is a diffusion process satisfying the stochastic differential equation with diffusion and drift coefficients $\sigma: \R^n\to \R^n\otimes \R^d$, $b: \R^n\to…

In the theory of lossy compression, the rate-distortion (R-D) function $R(D)$ describes how much a data source can be compressed (in bit-rate) at any given level of fidelity (distortion). Obtaining $R(D)$ for a given data source establishes…

A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such model is based on the expansion of the distribution function on a Hermite-Laguerre…

We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of…

We give a potential-theoretic characterization of priors which have the property that the corresponding Coulomb gas is "well-behaved" and similarly for more general Riesz gases. This means that the laws of the empirical measures of the…

In this paper, the aim of our work is to establish global weighted gradient estimates via fractional maximal functions and the point-wise regularity estimates of Dirichlet problem for divergence elliptic equations of the type \begin{align*}…

We consider vector-valued magnetic Schr\"odinger operators $-\bm \Delta_{\bm a}+V$ with magnetic potential $\bm a \in L^2_{\mathrm{loc}}(\mathbb{R}^d;\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries…