抄録
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
本文言語 | 英語 |
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ページ(範囲) | 417-423 |
ジャーナル | Bulletin of the American Mathematical Society |
巻 | 25 |
出版ステータス | 出版済み - 1991 |