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arXiv · 1212.3448

Self-avoiding walks and polygons -- an overview

Anthony J. Guttmann
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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.

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Anthony J. Guttmann. 2012-12-14. Self-avoiding walks and polygons -- an overview. https://arxiv.org/abs/1212.3448

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