19 citations · 98 across the 40 of their papers we have counts for
11 papers · 1 filter
Planar site percolation on semi-transitive graphs
Zhongyang Li
Semi-transitive graphs, defined in \cite{hps98} as examples where ``uniform percolation" holds whenever , are a large class of graphs more general than quasi-transitive grap…
Limit shape of perfect matchings on rail-yard graphs
Zhongyang Li
We obtain limit shape of perfect matchings on a large class of rail-yard graphs with right boundary condition given by the empty partition, and left boundary condition given by eit…
Weighted self-avoiding walks
Geoffrey R. Grimmett, Zhongyang Li
We study the connective constants of weighted self-avoiding walks (SAWs) on infinite graphs and groups. The main focus is upon weighted SAWs on finitely generated, virtually indica…
Self-avoiding walks and connective constants
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of a quasi-transitive graph is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on from a given starting vertex. We sur…
Cubic graphs and the golden mean
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of a graph is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. We investigate the validity of the ine…
Connective constants and height functions for Cayley graphs
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of an infinite transitive graph is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimm…
Locality of connective constants
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of a quasi-transitive graph is the exponential growth rate of the number of self-avoiding walks from a given origin. We prove a locality theorem…
Counting self-avoiding walks
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of a graph is the asymptotic growth rate of the number of self-avoiding walks on from a given starting vertex. We survey three aspects of the…
Strict inequalities for connective constants of transitive graphs
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of a graph is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. Strict inequalities are proved for connective con…
Bounds on connective constants of regular graphs
Geoffrey R. Grimmett, Zhongyang Li
Bounds are proved for the connective constant μ of an infinite, connected, Δ-regular graph G. The main result is that μ \ge \sqrt{Δ-1} if G is vertex-transitive and simple. This in…
Self-avoiding walks and the Fisher transformation
Geoffrey R. Grimmett, Zhongyang Li
The Fisher transformation acts on cubic graphs by replacing each vertex by a triangle. We explore the action of the Fisher transformation on the set of self-avoiding walks of a cub…