Brownian motion is a continuum scaling limit for a wide class of random processes, and
there has been great success in developing a theory for its properties (such as distribution …

A number of exact results have been obtained recently for the one-dimensional asymmetric
simple exclusion process, a model of particles which hop to their right at random times, on a …

The idea of writing up a book on the hydrodynamic behavior of interacting particle systems
was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the …

This book deals with one of the fundamental problems of nonequilibrium statistical
mechanics: the explanation of large-scale dynamics (evolution differential equations) from …

Several recent works have shown that the one-dimensional fully asymmetric exclusion
model, which describes a system of particles hopping in a preferred direction with hard core …

Interactive Particle Systems is a branch of Probability Theory with close connections to
Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T …

These lecture notes give a short review of methods such as the matrix ansatz, the additivity
principle or the macroscopic fluctuation theory, developed recently in the theory of non …

We consider the general problem of determining the steady state of stochastic
nonequilibrium systems such as those that have been used to model (among other things) …

Many complex systems of interacting particles that one encounters in nature behave on a
phenomenological level in some random fashion. Therefore the theoretical treatment of …

Publisher Summary This chapter discusses the systems coupled to two reservoirs of energy
in such a way that there is a steady energy flow through the system. An example is a resistor …