Critical behaviour of 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

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
元の言語英語
ページ（範囲）417-423
ジャーナルBulletin of the American Mathematical Society
巻25
出版物ステータス出版済み - 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

これを引用

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

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

研究成果: ジャーナルへの寄稿 › 記事

Hara, T & Slade, G 1991, 'Critical behaviour of self-avoiding walk in five or more dimensions.', Bulletin of the American Mathematical Society, 巻. 25, pp. 417-423.
Hara T, Slade G. Critical behaviour of self-avoiding walk in five or more dimensions. Bulletin of the American Mathematical Society. 1991;25:417-423.
Hara, Takashi ; Slade, Gordon. / Critical behaviour of self-avoiding walk in five or more dimensions. ：: Bulletin of the American Mathematical Society. 1991 ; 巻 25. pp. 417-423.
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