### Abstract

Original language | English |
---|---|

Pages (from-to) | 417-423 |

Journal | Bulletin of the American Mathematical Society |

Volume | 25 |

Publication status | Published - 1991 |

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### Cite this

*Bulletin of the American Mathematical Society*,

*25*, 417-423.

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

Research output: Contribution to journal › Article

*Bulletin of the American Mathematical Society*, vol. 25, pp. 417-423.

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TY - JOUR

T1 - Critical behaviour of self-avoiding walk in five or more dimensions.

AU - Hara, Takashi

AU - Slade, Gordon

PY - 1991

Y1 - 1991

N2 - 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

AB - 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

M3 - Article

VL - 25

SP - 417

EP - 423

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

SN - 0273-0979

ER -