Jacob van den Berg

CWI, Amsterdam (The Netherlands)

1st Floor Auditorium, CoRE Building
Rutgers University
Friday, February 28, 1997 at 11:30 am (Refreshments at 11:15 a.m.)

Percolation, mixing and coupling

Suppose we have a finite or countably infinite graph (e.g., the square or cubic lattice), and randomly remove edges or vertices. What can be said about the probability that, in the resulting (random) graph, there is a path between two given vertices, or the probability that a given vertex belongs to an infinite component?

Percolation theory deals with these and related questions, and was motivated by the need for simple but clarifying models of cooperative phenomena like the spread of infection in a population, or a gas through a porous medium.

A random spatial process (e.g., the process describing which nodes in a communication network are busy, or which spins in a magnetic material are `up' or `down') is called mixing if, roughly speaking, knowledge of the state of a given vertex gives almost no information about the states of remote vertices. Mixing is closely related to stability.

We will explain how percolation methods, combined with so-called coupling arguments, are useful in the study of mixing properties of an important class of models.

The emphasis of this talk is on intuitive ideas rather than mathematical formalism.

Document last modified on February 13, 1997