This work is devoted to the homogenization of elliptic equations in high-contrast media so-called `double-porosity' resonant regime, for which we solve two open problems literature random setting. First, prove qualitative under very weak conditions, that cover case inclusions are not uniformly bounded or separated. Second, stronger assumptions, provide sharp error estimates two-scale expansion.

This paper is concerned with the mean-field limit for gradient flow evolution of particle systems pairwise Riesz interactions, as number particles tends to infinity. Based on method introduced by Serfaty [Mean-Field Limits Gross--Pitaevskii and Parabolic Ginzburg--Landau equations, preprint, arXiv:1507.03821, 2015] in context vortices, using regularity stability properties limiting equation, we prove a result dimensions $1$ $2$ cases which this problem was still open.

Consider an ergodic stationary random field A on the ambient space ℝ d . In order to establish concentration properties for nonlinear functions Z(A), it is standard appeal functional inequalities like Poincaré or logarithmic Sobolev in probability space. These are however only known hold a restricted class of laws (product measures, Gaussian measures with integrable covariance, more general Gibbs nicely behaved Hamiltonians). this contribution, we introduce variants these inequalities, which...

This work is devoted to the definition and analysis of effective viscosity associated with a random suspension small rigid particles in steady Stokes fluid. While previous works on topic have conveniently assumed that are uniformly separated, we relax this restrictive assumption form mild moment bounds interparticle distances.

In the mean-field regime, evolution of a gas $N$ interacting particles is governed in first approximation by Vlasov type equation with self-induced force field. This conservative and describes return to equilibrium only very weak sense Landau damping. However, correction this given Lenard-Balescu operator, which dissipates entropy on long timescale $O(N)$. paper, we show how one can derive rigorously intermediate timescales (of order $O(N^r)$ for $r<1$), close equilibrium.

In a companion article we have introduced notion of multiscale functional inequalities for functions X(A) an ergodic stationary random field A on the ambient space R d .These are weighted versions standard Poincaré, covariance, and logarithmic Sobolev inequalities.They hold all examples fields arising in modelling heterogeneous materials applied sciences whereas their much more restrictive.In this contribution first investigate link between decorrelation or mixing properties fields.Next,...

Consider a linear elliptic partial differential equation in divergence form with random coefficient field. The solution-operator displays fluctuations around its expectation. recently-developed pathwise theory of stochastic homogenization reduces the characterization these to those so-called standard commutator. In this contribution, we investigate scaling limit key quantity: starting from Gaussian-like field possibly strong correlations, establish convergence rescaled commutator fractional...

This work develops a quantitative homogenization theory for random suspensions of rigid particles in steady Stokes flow, and completes recent qualitative results. More precisely, we establish large-scale regularity this problem, prove moment bounds the associated correctors optimal estimates on error; latter further requires ergodicity assumption suspension. Compared to corresponding divergence-form linear elliptic equations, substantial difficulties arise from analysis fluid...

Since its early beginnings, mankind has put to test many different society forms, and this fact raises a complex of interesting questions. The objective paper is present general population model which takes essential features any into account gives answers on the basis only two natural hypotheses. One that societies want survive, second, individuals in would, general, like increase their standard living. We start by presenting mathematical model, may be seen as particular type controlled...

A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of parameter in a location family is sample mean for all samples sizes if and only Gaussian. There exist many extensions this result diverse directions, most them focussing on scale families. In paper, we propose unified treatment literature by providing general MLE theorems one-parameter group families (with particular attention parameters). doing so, provide tools determining whether or...

In a recent work, Bourgain gave fine description of the expectation solutions discrete linear elliptic equations on Zd with random coefficients in perturbative regime using tools from harmonic analysis. This result is surprising for it goes beyond expected accuracy suggested by results quantitative stochastic homogenization. this short article we reformulate Bourgain's form that highlights its interest to state-of-the-art homogenization (and especially theory fluctuations), and state several...