Large ensembles of stochastically evolving interacting particles describe phenomena in
diverse fields including statistical physics, neuroscience, biology, and engineering. In such …

This volume collects ten surveys on the modeling, simulation, and applications of active
particles using methods ranging from mathematical kinetic theory to nonequilibrium …

Abstract Interacting Particle Systems—exemplified by the voter model, iterative majority, and
iterative k—majority processes—have found use in many disciplines including distributed …

A central and fundamental issue in the theory of complex systems is to understand how local
rules lead to collective behavior of the whole system. This paper will investigate a typical …

In the thesis we study exact solutions to simple interacting non-equilibrium problems. We
propose two lattice models in discrete time, a model of hard-core interacting charged …

Consider a finite system of rank-based competing Brownian particles, where the drift and
diffusion of each particle depend only on its current rank relative to other particles. We …

Controlling large particle systems in collective dynamics by a few agents is a subject of high
practical importance, eg, in evacuation dynamics. In this paper we study an instantaneous …

We study the Fleming--Viot particle system in a discrete state space, in the regime of a fast
selection mechanism, namely with killing rates which grow to infinity. This asymptotics …

We consider a model for interacting objects, where the evolution of each object is given by a
finite state Markov chain, whose transition matrix depends on the present and the past of the …

Given a large number of homogeneous players that are distributed across three possible
states, we consider the problem in which these players have to control their transition rates …