The Philosophers' Process: An Ergodic Reversible Nearest Particle System

The Reversible Nearest Particle System on a Finite Set ∗

In this paper we study the one-parameter family of attractive reversible nearest particle systems on {1, 2, · · · , N}. Denote by σN the time that the system first hits the empty set. Then, σN has a logarithmic increasing rate as the parameter λ is small enough, but an exponential increasing rate as λ is large enough. Especially, it has a polynomial increasing rate in the critical case, i.e. λ ...

The Reversible Nearest Particle System on a Finite Interval ∗

In this paper we study a one-parameter family of attractive reversible nearest particle system on a finite interval. As the length of the interval increases, the time that the nearest particle system first hits the empty set increases in different order, from logarithmic to exponential, according to the intensity of interaction. In particular, at the critical case, the first hitting time increa...

When is an Interacting Particle System Ergodic?

We consider stochastic flip dynamics for an infinite number of Ising spins on the lattice Έ. We find a sequence of constructive criteria for the system to be exponentially ergodic. The main idea is to approximate the continuous time process with discrete time processes (its Euler polygon) and to use an improved version of previous results [MS] about constructive ergodicity of discrete time proc...

The Philosophers ' Process

The Philosophers' Process is a Markovian version of the famous Dining Philosophers Problem introduced by Dijkstra as a model for resource sharing. It can be viewed as a reversible interacting particle system. This paper deals with the problem of computing its reversible measure in the case of a large but nite number of sites. This equilibrium measure is a Markov eld on the underlying graph of i...

The Philosophers' Process on Graphs