Related papers: Competing particle systems evolving by interacting…
This review article discusses limit distributions and variance bounds for particle current in several dynamical stochastic systems of particles on the one-dimensional integer lattice: independent particles, independent particles in a random…
Most of the published articles on random motions have been devoted to the study of the telegraph process or its generalizations that describe the random motion in $R^n$ of a single particle in a Markov or semi-Markov medium. However, up to…
For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it…
We construct birth-and-death Markov evolution of states(distributions) of point particle systems in $\mathbb{R}^d$. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…
We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…
We consider a process $Z$ on the real line composed from a L\'evy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of $Z$ seen from its supremum, the supremum $\overline Z$…
In cellular vortical flows, namely arrays of counter-rotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semi-rigid…
In this article we study a system of $N$ particles, each of them being defined by the couple of a position (in $\mathbb{R}^d$) and a so-called orientation which is an element of a compact Riemannian manifold. This orientation can be seen as…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…
In many real-world scenarios, the underlying random fluctuations are non-Gaussian, particularly in contexts where heavy-tailed data distributions arise. A typical example of such non-Gaussian phenomena calls for L\'evy noise, which…
Population dynamics of individuals undergoing birth and death and diffusing by short or long ranged twodimensional spatial excursions (Gaussian jumps or L\'{e}vy flights) is studied. Competitive interactions are considered in a global case,…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…