Generalized approach to the non-backtracking lace expansion

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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 $d\geq 21$.
Originele taal-2Engels
Uitgeverijs.n.
Aantal pagina's65
StatusGepubliceerd - 2015

Publicatie series

NaamarXiv
Volume1506.07969 [math.PR]

Vingerafdruk

expansion
animals

Citeer dit

@book{28943d3d623d4e469687368d9c4d5d91,
title = "Generalized approach to the non-backtracking lace expansion",
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 $d\geq 21$.",
author = "R.J. Fitzner and {Hofstad, van der}, R.W.",
year = "2015",
language = "English",
series = "arXiv",
publisher = "s.n.",

}

Generalized approach to the non-backtracking lace expansion. / Fitzner, R.J.; Hofstad, van der, R.W.

s.n., 2015. 65 blz. (arXiv; Vol. 1506.07969 [math.PR]).

Onderzoeksoutput: Boek/rapportRapportAcademic

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N2 - 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 $d\geq 21$.

AB - 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 $d\geq 21$.

UR - https://arxiv.org/abs/1506.07969

M3 - Report

T3 - arXiv

BT - Generalized approach to the non-backtracking lace expansion

PB - s.n.

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