Related papers: Convergence to equilibrium in a class of interacti…

We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…

We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is based upon a sharp estimate on the relative…

Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes,…

We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…

Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…

Synchronization in networks of discrete-time linear time-invariant systems is considered under relative actuation. Neither input nor output matrices are assumed to be commensurable. A distributed algorithm that ensures synchronization via…

We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…

Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schr\"odinger equation together with its conservation laws. Surprisingly, a whole class of…

We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…

We study a discrete-time interacting particle system with continuous state space which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin…

We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive and negative. Same-sign particles repel each other, and…

We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…

We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…

John H. Conway's Game of Life, as well as cellular automata in the larger family of Life-like CA, are discrete: the cells have a binary state space and the birth and survival transition rules are 9-bits apiece. Inspired by Life, several…

We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…

We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…

Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows…