Related papers: An informal introduction to quantitative stochasti…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar…
We study homogenization problem for the stationary Maxwell system. It is supposed that the magnetic permeability and the dielectric permittivity locally close to fast-oscillating (with respect to some small parameter) periodic functions…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…
We investigate depoissonization, the problem of recovering asymptotics of sequence coefficients from their exponential generating function. Classical approaches rely on complex-analytic growth conditions, but here we develop real-variable…
Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
This paper is devoted to the study of the stochastic-periodic homogenization of Poisson-Nernst-Planck equations in porous media. It is shown by the stochastic two-scale convergence method extended to periodic surfaces that results in a…
The aim of the course is to lead to an understanding of homogenisation processes in an operator-theoretic sense. In fact, using solely operator-theoretic means not referring to the particular form of the coefficients, we will identify an…
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…