Critical behaviour of self-avoiding walk in five or more dimensions.

Takashi Hara, Gordon Slade

Research output: Contribution to journalArticle

Abstract

We use the lace expansion to prove that in five or more dimensions the standard self-avoiding walk on the hypercubic lattice behaves in many respects like the simple random walk. In particular, it is shown that the leading asymptotic behaviour of the number of n-step self-avoiding walks is purely exponential, that the mean-square displacement is asymptotically linear in the number of steps, and that the scaling limit is Gaussian, in the sense of convergence in distribution to Brownian motion. A number of related results are also
Original languageEnglish
Pages (from-to)417-423
JournalBulletin of the American Mathematical Society
Volume25
Publication statusPublished - 1991

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Self-avoiding Walk
Brownian movement
Critical Behavior
Lace Expansion
Convergence in Distribution
Asymptotically Linear
Simple Random Walk
Scaling Limit
Mean Square
Brownian motion
Asymptotic Behavior

Cite this

Critical behaviour of self-avoiding walk in five or more dimensions. / Hara, Takashi; Slade, Gordon.

In: Bulletin of the American Mathematical Society, Vol. 25, 1991, p. 417-423.

Research output: Contribution to journalArticle

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