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math.PR2024
Critical site percolation and cutsets
Zhongyang Li
In 2003, Kahn conjectured a characterization of the critical percolation probability in terms of vertex cut sets (\cite{JK03}). Later, Lyons and Peres (2016) conjectured a si…
math.PR2024
Independent GUE minor processes of perfect matchings on rail-yard graphs
Zhongyang Li
We study perfect matchings on the rail-yard graphs in which the right boundary condition is given by the empty partition and the left boundary can be divided into finitely many alt…
math.PR2024
Perfect Matchings and Essential Spanning Forests in Hyperbolic Double Circle Packings
Zhongyang Li
We investigate perfect matchings and essential spanning forests in planar hyperbolic graphs via circle packings. We prove the existence of nonconstant harmonic Dirichlet functions…