Self-Avoiding Walks and Amenability

[摘要] The connective constant $\mu(G)$ of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. The relationship between connective constants and amenability is explored in the current work.

[学科分类] 离散数学和组合数学

[关键词] Self-avoiding walk;Connective constant;Cayley graph;Amenable group;Elementary amenable group;Indicable group;Grigorchuk group;Higman group;Baum