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We carry out the asymptotic analysis of repulsive ensembles of N particles which are discrete analogues of continuous 1d log-gases or beta-ensembles of random matrix theory. The ensembles that we study have several groups of particles which…
One of the main features of statistical systems out of equilibrium is the currents they exhibit in their stationary state: microscopic currents of probability between configurations, which translate into macroscopic currents of mass,…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…
We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
In multicomponent systems with strong local interaction one can encounter some phenomena absent in the standard systems of statistical physics and other multicomponent systems. Namely, a system with $N$ components in the bounded volume of…
In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…
A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal…
Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the…
We consider a two species process which evolves in a finite or infinite domain in contact with particles reservoirs at different densities, according to the superposition of a generalised contact process and a rapid-stirring dynamics in the…
We consider macroscopic descriptions of particles where repulsion is modelled by non-linear power-law diffusion and attraction by a homogeneous singular kernel leading to variants of the Keller-Segel model of chemotaxis. We analyse the…
In this paper, we study the dynamics of a system of $n$ coupled, self-propelled particles: $\ddot r_k = (\alpha-\beta |\dot r_k|^2)\dot r_k - \frac{\gamma}{n}\sum_{m=1}^n(r_k-r_m)$, $r_k\in \mathbb R^2.$ Numerical experiments indicate that,…
Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
This pedagogical review addresses several issues related to statistical description of gravitating systems in both static and expanding backgrounds, focusing on the latter. After briefly reviewing the results for the static background, I…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…