19 citations · 98 across the 40 of their papers we have counts for
4 papers · 1 filter
Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices
Cédric Boutillier, Zhongyang Li
We study asymptotics of perfect matchings on a large class of graphs called the contracting square-hexagon lattice, which is constructed row by row from either a row of a square gr…
Constrained percolation, Ising model and XOR Ising model on planar lattices
Zhongyang Li
We study constrained percolation models on planar lattices including the lattice and the square tilings of the hyperbolic plane, satisfying certain local constraints on…
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…
Mixing time of Markov chains for the 1-2 model
Zhongyang Li
A 1-2 model configuration is a subset of edges of a hexagonal lattice satisfying the constraint that each vertex is incident to 1 or 2 edges. We introduce Markov chains to sample t…