Article thumbnail

Generalized approach to the non-backtracking lace expansion

By RJ Robert Fitzner and RW Remco van der Hofstad

Abstract

The lace expansion is a powerful perturbative technique to analyze the critical behavior of random spatial processes such as the self-avoiding walk, percolation and lattice trees and animals. The non-backtracking lace expansion (NoBLE) is a modification that allows us to improve its applicability in the nearest-neighbor setting on the $\Zd$-lattice for percolation, lattice trees and lattice animals. The NoBLE gives rise to a recursive formula that we study in this paper at a general level. We state assumptions that guarantee that the solution of this recursive formula satisfies the infrared bound. In two related papers, we show that these conditions are satisfied for percolation in $d\geq 11$, for lattice trees in $d\geq 16$ and for lattice animals in $d\geq 21$

Publisher: s.n.
Year: 2015
OAI identifier: oai:library.tue.nl:890481
Provided by: Repository TU/e
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://repository.tue.nl/89048... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.