Related papers: Direct Interaction Approximation for generalized s…
We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the $L^2$-speed of convergence of the empirical density of states in a…
Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when…
The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in…
We study the mixing time of Glauber dynamics for Ising models in which the interaction matrix contains a single negative spectral outlier. This class includes the anti-ferromagnetic Curie-Weiss model, the anti-ferromagnetic Ising model on…
We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod…
We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
The paper is devoted to the optimal control of a system with two time-scales, in a regime when the limit equation is not of averaging type but, in the spirit of Wong-Zakai principle, it is a stochastic differential equation for the slow…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
In anisotropic turbulence the correlation functions are decomposed in the irreducible representations of the SO(3) symmetry group (with different "angular momenta" $\ell$). For different values of $\ell$ the second order correlation…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…
We discuss a stochastic interacting particles' system connected to dyadic models of turbulence, defining suitable classes of solutions and proving their existence and uniqueness. We investigate the regularity of a particular family of…
Standard eddy viscosity models, while robust, cannot represent backscatter and have severe difficulties with complex turbulence not at statistical equilibrium. This report gives a new derivation of eddy viscosity models from an equation for…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…
Developing physically consistent closure models is a longstanding challenge in simulating plasma turbulence, even in minimal systems such as the two-field Hasegawa-Wakatani (HW) model, which captures essential features of drift-wave…
We show that Tsallis ensemble of power-law distributions provides a mechanical model of nonextensive equilibrium thermodynamics for small interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature, we prove that it is an…
The paper proposes a new stochastic intervention control model conducted in various commodity and stock markets. The essence of the phenomenon of intervention is described in accordance with current economic theory. A review of papers on…
We introduce and study stochastic $N$-particle ensembles which are discretizations for general-$\beta$ log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, $(z,w)$-measures, etc. We…