# CSM

## Seminar

### Prudent and quasi-prudent self-avoiding walks and polygons

Seminar Room 1, Newton Institute

#### Abstract

Prudent self-avoiding walks and quasi-prudent self-avoiding walks are proper subsets of self-avoiding walks in dimension 2 or greater. Prudent SAW are not allowed to take a step in a direction which, if continued, would encounter a previously visited vertex. Quasi-prudent walks are self-avoiding walks where a step to a neighbouring vertex v can only be taken if there is a prudent way to escape from v (in other words, if v can be seen from infinity). Polygon versions of the walks can be defined as walks (prudent or quasi-prudent) which end at a vertex adjacent to their starting point.

A variety of results, both rigorous and numerical, will be given for these models, mainly for two-dimensional walks, but we also have some preliminary results for walks on a three-dimensional lattice.

#### Video

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