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

Takashi Hara, Gordon Slade

Research output: Contribution to journalArticlepeer-review


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
Publication statusPublished - 1991


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