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Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
In this paper we study the effect of randomness in kinetic equations that preserve mass. Our focus is in proving the analyticity of the solution with respect to the randomness, which naturally leads to the convergence of numerical methods.…
The optimistic gradient method has seen increasing popularity for solving convex-concave saddle point problems. To analyze its iteration complexity, a recent work [arXiv:1906.01115] proposed an interesting perspective that interprets this…
We study a semilinear elliptic equation with a pure power nonlinearity with exponent $p>1$, and provide sufficient conditions for the existence of positive solutions. These conditions involve expected exit times from the domain, $D$, where…
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes…
For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these…
This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and…
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation…
The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of…
General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…
We provide a linear analysis on normal modes of the spin Boltzmann equation proposed in \cite{Weickgenannt:2021cuo}, where the non-diagonal or polarized part of the transition rate is neglected to ensure the Hermitian property of linearized…
Recently, a new class of semi-Lagrangian methods for the BGK model of the Boltzmann equation has been introduced [8, 17, 18]. These methods work in a satisfactory way either in rarefied or fluid regime. Moreover, because of the…
This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…
We study self-similar solutions of NLS-type dynamical systems. Lagrangian approach is used to show that they can be reduced to three canonical forms, which are related by Miura transformations. The fourth Painleve equation (PIV) is central…
In a previous work (Akian, Fodjo, 2016), we introduced a lower complexity probabilistic max-plus numerical method for solving fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite…
The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…