Related papers: Long time behavior of stochastic hard ball systems
We derive a model that describes the motion of a Brownian particle in a system which is dominated by gravitational forces. An example of such a system is a massive black hole immersed in a cluster of stars. We compute the dispersion in the…
The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes, are calculated in the long wavelength limit for a granular gas. The transport…
A field-theoretic approach is applied to describe behavior of three-dimensional, weakly disordered, elastically isotropic, compressible systems with long-range interactions at various values of a long-range interaction parameter.…
The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven…
The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with $H\in (1/2,1)$. We would like to emphasize that we do not use the usual cohomology…
In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in…
A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic barrier…
We calculate, numerically, the residence times (and their distribution) of a Brownian particle in a two-well system under the action of a periodic, saw-tooth type, external field. We define hysteresis in the system. The hysteresis loop area…
Via computer simulations we study evolution dynamics in systems of continuously moving Active Brownian Particles. The obtained results are discussed against those from the passive 2D Ising case. Following sudden quenches of uniform…
We study space-time fluctuations of a hard sphere system at thermal equilibrium, and prove that the covariance converges to the solution of a linearized Boltzmann equation in the low density limit, globally in time. This result has been…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
In this paper we consider an interacting particle system in $\mathbb{R}^d$ modelled as a system of $N$ stochastic differential equations driven by L\'evy processes. The limiting behaviour as the size $N$ grows to infinity is achieved as a…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
We derive the probability density function of the positive occupation time of one-dimensional Brownian motion with two-valued drift. Long time asymptotics of the density are also computed. We use the result to describe the transitional…
A field-theoretic description of critical behavior of Ising systems with long-range interactions is obtained in the two-loop approximation directly in the three-dimensional space. It is shown that long-range interactions affect the…
We consider convergence properties of the long-term behaviors with respect to the coefficient of the stochastic term for a nonautonomous stochastic $p$-Laplacian lattice equation with multiplicative noise. First, the upper semi-continuity…
We consider a basic stochastic particle system consisting of $N$ identical particles with isotropic $k$-particle synchronization, $k\geq 2$. In the limit when both number of particles $N$ and time $t=t(N)$ grow to infinity we study an…
In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.
It has been known since Lanford [19] that the dynamics of a hard sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to…
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion we introduce a basis that…