Related papers: An informal introduction to quantitative stochasti…
Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n.…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
In this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a $\Lambda$-convex energy functional featuring random and rapidly…
We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field…
The four types of homogeneity -- additive, multiplicative, exponential, and logarithmic -- are generalized as transformations describing how a function $f$ changes under scaling or shifting of its arguments. These generalized homogeneity…
We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…
Stochastic Rounding is a probabilistic rounding mode that is surprisingly effective in large-scale computations and low-precision arithmetic. Its random nature promotes error cancellation rather than error accumulation, resulting in slower…
This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new results are also presented, and several problems are posed.
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
We study renormalization group flows in far-from-equilibrium states. The study is made tractable by focusing on states that are spatially homogeneous, time-independent, and scale-invariant. Such states, in which mode $k$ has occupation…
This article studies some numerical approximations of the homogenized matrix for stochastic linear elliptic partial differential equations in divergence form. We focus on the case when the underlying random field is a small perturbation of…
This paper investigates the quantitative homogenization of first-order ODEs. For single-scale scalar ODEs, we obtain a sharp $O(\varepsilon)$ convergence rate and characterize the effective constant. In the multi-scale setting, our results…
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…
In this paper we investigate the homogenization problem with a non-homogeneous Dirichlet condition. Our aim is to give error estimates with boundary data in $H^{1/2}(\partial\Omega)$. The tools used are those of the unfolding method in…
This work is a follow-up to our previous work "A numerical approach related to defect-type theories for some weakly random problems in homogenization" (preprint available on this archive). It extends and complements, both theoretically and…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…