Related papers: Quantitative homogenization of degenerate random e…
We study several basic dispersive models with random periodic initial data such that the different Fourier modes are independent random variables. Motivated by the vast Physics literature on related topics, we then study how much the…
We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
We use a generalization of Hoeffding's inequality to show concentration results for the free energy of disordered pinning models, assuming only that the disorder has a finite exponential moment. We also prove some concentration inequalities…
We study the random conductance model on the lattice $\mathbb{Z}^d$, i.e. we consider a linear, finite-difference, divergence-form operator with random coefficients and the associated random walk under random conductances. We allow the…
Within the framework of the algebra of canonical commutation relations in Euclidean space, a long range order between particles in bounded regions is established in states with a sufficiently large particle number. It occurs whenever…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is…
In order to characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine learning method to characterize…
This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. In [11] rate of convergence results in…
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double bracket dissipation in kinetic equations using an oriented…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed…
In this paper, we present an abstract framework to obtain convergence rates for the approximation of random evolution equations corresponding to a random family of forms determined by finite-dimensional noise. The full discretization error…
We show how the dispersive regime of the Jaynes-Cummings model may serve as a valuable tool to the study of open quantum systems. We employ it in a bottom-up approach to build an environment that preserves qubit energy and induces varied…