7 citations · 15 across the 13 of their papers we have counts for
10 papers · 1 filter
Percolation on Bidirected Graphs
Yucheng Liu, Leonardo T. Rolla, Yuliang Shi
We study bidirected percolation on an undirected graph : each edge is replaced by two oppositely directed edges, each of which is open independently with probability . Two ve…
Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation
Yucheng Liu, Gordon Slade
The study of the Ornstein--Zernike decay of subcritical two-point functions in equilibrium statistical mechanics has a history going back over a century. Despite this, the crossove…
Decay of connection probability in high-dimensional continuum percolation
Matthew Dickson, Yucheng Liu
We study a percolation model on called the random connection model. For large, we use the lace expansion to prove that the critical two-point connection probabili…
High-dimensional long-range statistical mechanical models have random walk correlation functions
Yucheng Liu
We consider long-range percolation, Ising model, and self-avoiding walk on , with couplings decaying like where , above the upper critical…
Near-critical and finite-size scaling for high-dimensional lattice trees and animals
Yucheng Liu, Gordon Slade
We consider spread-out models of lattice trees and lattice animals on , for above the upper critical dimension . We define a correlation length an…
Critical scaling profile for trees and connected subgraphs on the complete graph
Yucheng Liu, Gordon Slade
We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a…
Gaussian deconvolution on with application to self-repellent Brownian motion
Yucheng Liu
We consider the convolution equation on , , where is the Dirac delta function and are given functions. We provide conditions on …
A general approach to massive upper bound for two-point function with application to self-avoiding walk torus plateau
Yucheng Liu
We prove a sufficient condition for the two-point function of a statistical mechanical model on , , to be bounded uniformly near a critical point by $|x|^{-(d-…
Gaussian deconvolution and the lace expansion for spread-out models
Yucheng Liu, Gordon Slade
We present a new proof of decay of critical two-point functions for spread-out statistical mechanical models on above the upper critical dimension, ba…
Gaussian deconvolution and the lace expansion
Yucheng Liu, Gordon Slade
We give conditions on a real-valued function on , for , which ensure that the solution to the convolution equation has Gaussian deca…