Hydrodynamic behavior and interacting particle systems

Interacting particle systems: hydrodynamic limit versus high density limit

In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach for different scenarios: the law of large numbers, the central limit theorem, and the large deviations principle. It is given a special attention to a recen...

Diffusive Behavior of Interacting Particle Systems

Interacting Particle Systems

3 4 CONTENTS Preface Interacting particle systems, in the sense we will be using the word in these lecture notes, are countable systems of locally interacting Markov processes. Each interacting particle system is define on a lattice: a countable set with (usually) some concept of distance defined on it; the canonical choice is the d-dimensional integer lattice Z d. On each point in this lattice...

Interacting particle systems

2 The asymmetric simple exclusion process 18 2.1 Stationary measures and conserved quantities . . . . . . . . . . . . . . . . . . . 18 2.2 Currents and conservation laws . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Hydrodynamics and the dynamic phase transition . . . . . . . . . . . . . . . . . 26 2.4 Open boundaries and matrix product ansatz . . . . . . . . . . . . . . . . . . ...

Interacting Particle Systems Approximations ofthe

In this paper we consider the continuous time ltering problem and we estimate the order of convergence of an interacting particle system scheme presented by the authors in previous works. We will discuss how the discrete time approximating model of the Kushner-Stratonovitch equation and the genetic type interacting particle system approximation combine. We present quenched error bounds as well ...