The lace expansion for self-avoiding walk in five or more dimensions.

Takashi Hara, Gordon Slade

研究成果: ジャーナルへの寄稿記事

抄録

This paper is a continuation of our companion paper [16], in which it was proved that the standard model of self-avoiding walk in five or more dimensions has the same critical behaviour as the simple random walk, assuming convergence of the lace expansion. We prove the convergence of the lace expansion, an upper and lower infrared bound, and a number of other estimates that were used in the companion paper. The proof requires a good upper bound on the critical point (or equivalently a lower bound on the connective constant). In an appendix, new upper bounds on the critical point in dimensions higher than two are obtained, using elementary methods which are independent of the lace expansion. The proof of convergence of the lace expansion is computer assisted. Numerical aspects of the proof, including methods for the numerical evaluation of simple random walk quantities such as the two-point function (or lattice Green function), are treated in an appendix.
元の言語英語
ページ(範囲)235-327
ジャーナルReviews in Mathematical Physics
4
出版物ステータス出版済み - 1992

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Lace Expansion
Self-avoiding Walk
Simple Random Walk
expansion
random walk
Critical point
critical point
Upper bound
Critical Behavior
Higher Dimensions
Continuation
Standard Model
Green's function
Infrared
Green's functions
Lower bound
evaluation
Evaluation
estimates
Estimate

これを引用

The lace expansion for self-avoiding walk in five or more dimensions. / Hara, Takashi; Slade, Gordon.

:: Reviews in Mathematical Physics, 巻 4, 1992, p. 235-327.

研究成果: ジャーナルへの寄稿記事

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