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Tree embeddings and nonuniqueness in site percolation
Zhongyang Li
We prove a nonuniqueness theorem for Bernoulli site percolation on properly embedded planar graphs (graphs that can be embedded into $\RR^2$ with no accumulation points), and we ob…
Doubly Free-Boundary Rail-Yard Dimers and Annular Gaussian Fluctuations
Zhongyang Li
We study rail-yard dimer measures with free boundary conditions at both the left and the right boundary. The double free-boundary geometry produces an infinite family of reflected…
Matchings on Random Regular Hypergraphs
Zhongyang Li
We study the monomer--dimer partition function on the configuration model of random -regular, -uniform hypergraphs. For fixed , we prove quenched free-energy limits…
Hyperbolic site percolation
Geoffrey R. Grimmett, Zhongyang Li
Several results are presented for site percolation on quasi-transitive, planar graphs with one end, when properly embedded in either the Euclidean or hyperbolic plane. If $(G_1…