Publications (61)
New Lower Bounds on the Self-Avoiding-Walk Connective Constant
Takashi Hara, Gordon Slade, Alan D. Sokal
We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice . The method is based on loop…
An extension of the inductive approach to the lace expansion
Remco van der Hofstad, Mark Holmes, Gordon Slade
We extend the inductive approach to the lace expansion, previously developed to study models with critical dimension 4, to be applicable more generally. In particular, the result o…
The scaling limit of the incipient infinite cluster in high-dimensional percolation. I. Critical exponents
Takashi Hara, Gordon Slade
This is the first of two papers on the critical behaviour of bond percolation models in high dimensions. In this paper, we obtain strong joint control of the critical exponents eta…
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…
Three-dimensional tricritical spins and polymers
Roland Bauerschmidt, Martin Lohmann, Gordon Slade
We consider two intimately related statistical mechanical problems on : (i) the tricritical behaviour of a model of classical unbounded -component continuous spins…
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 dec…