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 …

Recent work on stochastic interacting particle systems with two particle species (or single-
species systems with kinematic constraints) has demonstrated the existence of spontaneous …

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 …

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 …

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 …

We consider the asymmetric simple exclusion process (ASEP) with open boundaries and
other driven stochastic lattice gases of particles entering, hopping and leaving a one …

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally
asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit …

Interacting particle systems is by now a mature area of probability theory, but one that is still
very active. We begin this paper by explaining how models from this area arise in fields such …

We prove a duality between the asymmetric simple exclusion process (ASEP) with non-
conservative open boundary conditions and an asymmetric exclusion process with particle …

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system
of particles which jump at rates p and 1-p (here p> 1/2) to adjacent empty sites on their right …