6 papers · 1 filter
A random walk approach to high-dimensional critical phenomena
Hugo Duminil-Copin, Aman Markar, Romain Panis +1
We present a "black box" proof of mean-field near-critical behaviour for a family of functions on () satisfying a short list of assumptions. The functions repr…
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…
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 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…