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We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…

The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…

We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…

Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different…

Depletion interactions between colloidal particles dispersed in a fluid medium are effective interactions induced by the presence of other types of colloid. They are not instantaneous but build up in time. We show by means Brownian dynamics…

We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative…

Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup…

We consider a purely harmonic chain of oscillators which is perturbed by a stochastic noise. Under this perturbation, the system exhibits two conserved quantities: the volume and the energy. At the level of the hydrodynamic limit, under…

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is derived…

Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…

In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…

We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…

Diffusion coefficient usually decreases when friction increases. We analyze the opposite behavior in the paradigmatic system consisting of an inertial Brownian particle moving in a symmetric spatially periodic potential and driven by an…

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the…

We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

We study a one-dimensional hamiltonian chain of masses perturbed by an energy conserving noise. The dynamics is such that, according to its hamiltonian part, particles move freely in cells and interact with their neighbors through…

We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision.…

We study systems of interacting Brownian particles in one dimension constructed as the diffusion scaling limits of Fisher's vicious walk models. We define two types of nonintersecting Brownian motions, in which we impose no condition (resp.…

We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For…