CRM-Fields-PIMS Prize Lecture 2010: The Self-Avoiding Walk

Simple random walk is well understood. However, if we condition a random walk not to intersect itself, so that it is a self-avoiding walk, then it is much more difficult to analyze and many of the important mathematical problems remain unsolved.

This lecture will give an overview of some of what is known about the self-avoiding walk, including some old and some more recent results, using methods that touch on combinatorics, probability, and statistical mechanics.