9 papers · 1 filter
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 critica…
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-…
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…
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…