8 papers · 1 filter
A Randomized Approximation Algorithm for Doubly Free-Boundary Macdonald Processes
Zhongyang Li
We construct an approximate sampler for finite doubly free-boundary Macdonald rail-yard processes with Macdonald, boundary, and edge parameters in . The construction allows…
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…
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…
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…
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…
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…
Asymptotics of Bounded Lecture-Hall Tableaux
David Keating, Zhongyang Li, Istvan Prause
We study weighted bounded \(n\)-lecture hall tableaux with bound \(t_n\) in the joint limit \(n,t_n\to\infty\) with \(t_n/n\toα\in(0,\infty)\). Using their non-intersecting-path re…