6 papers · 1 filter
Limit shape of perfect matchings on contracting bipartite graphs
Zhongyang Li
We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic…
Asymptotics of Schur functions on almost staircase partitions
Zhongyang Li
We study the asymptotics of Schur polynomials with partitions which are almost staircase; more precisely, partitions that differ from b…
Ising Percolation on Nonamenable Planar Graphs
Zhongyang Li
We study infinite ``'' or ``'' clusters for an Ising model on an connected, transitive, non-amenable, planar, one-ended graph with finite vertex degree. If the critical p…
Exact Recovery of Community Detection in k-partite Graph Models
Zhongyang Li
We study the vertex classification problem on a graph whose vertices are in different communities, edges are only allowed between distinct communities, and the numbe…
Fluctuations of dimer heights on contracting square-hexagon lattices
Zhongyang Li
We study perfect matchings on the square-hexagon lattice with periodic edge weights such that the boundary condition is given by either (1) each remaining vertex on the…
Uniqueness of Infinite Homogeneous Clusters in 1-2 Model
Zhongyang Li
A 1-2 model configuration is a subset of edges of the hexagonal lattice such that each vertex is incident to one or two edges. We prove that for any translation-invariant Gibbs mea…