Self-avoiding walks on graphs and groups
Seminar | January 25 | 3:10-4 p.m. | 1011 Evans Hall
Geoffrey Grimmett, Cambridge University
The problem of self-avoiding walks (SAWs) arose in statistical mechanics in the 1940s, and has connections to probability, combinatorics, and the geometry of groups. The basic question is to count SAWs. The so-called 'connective constant' is the exponential growth rate of the number of n-step SAWs. We summarise joint work with Zhongyang Li concerned with the question of how the connective constant depends on the choice of graph. This work includes equalities and inequalities for connective constants, and a partial answer to the so-called 'locality problem' for graphs and particularly Cayley graphs.