6 papers
Recursive Packing Bounds for Supercritical Disconnection in Bernoulli Site Percolation
Zhongyang Li
For Bernoulli site percolation on an infinite, connected, locally finite graph , we obtain quantitative upper bounds on the supercritical disconnection probability \[ \mat…
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…
Self-avoiding walks on cubic graphs and local transformations
Benjamin Grant, Zhongyang Li
Despite its elementary definition, the self-avoiding walk (SAW) poses notoriously hard enumerative problems: exact connective constants are known for only a handful of infinite gra…
Planar Site Percolation, End Structure, and the Benjamini-Schramm Conjecture
Zhongyang Li
Let be an infinite, connected, locally finite planar graph and consider i.i.d.\ Bernoulli site percolation. Write and for…
Doubly Free-Boundary Macdonald Processes: Reflection Identities and Jack Asymptotics
Zhongyang Li, Kaili Shi
We introduce a doubly free-boundary Macdonald process on rail-yard interlacings and develop a reflection calculus for its observables. Boundary Cauchy--Littlewood identities, combi…
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…