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math-ph2000
Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models
Takashi Hara, Remco van der Hofstad, Gordon Slade
We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and bond lattice animals on the d-dimensional hyper cubic lattice having long finite-range conn…
math-ph1999
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…
math-ph1998
The incipient infinite cluster in high-dimensional percolation
Takashi Hara, Gordon Slade
We announce our recent proof that, for independent bond percolation in high dimensions, the scaling limits of the incipient infinite cluster's two-point and three-point functions a…