Self-avoiding walks and polygons -- an overview
Abstract
This is a rather personal review of the problem of self-avoiding walks and polygons. After defining the problem, and outlining what is known rigorously and what is merely conjectured, I highlight the major outstanding problems. I then give several applications in which the I have been involved. These include a study of surface adsorption of polymers, counting possible paths in a telecommunication network, hitting probabilities of SAWs in a rectangle, and the modelling of biological experiments on polymers. I hope to show that SAWs are not only of intrinsic mathematical interest, but also have many interesting and useful applications.
Keywords
Cite
@article{arxiv.1212.3448,
title = {Self-avoiding walks and polygons -- an overview},
author = {Anthony J. Guttmann},
journal= {arXiv preprint arXiv:1212.3448},
year = {2012}
}
Comments
This is a slightly updated and expanded version, with minor corrections, of an article that first appeared in the October 2012 issue of the Asia Pacific Newsletter, accompanying an interview with the author. 19 pages, 9 figures