The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions

Takashi Hara, Gordon Slade

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)

Abstract

We prove the existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on ℤd. For the critical point, defined as the reciprocal of the connective constant, the coefficients of the expansion are computed through order d−6, with a rigorous error bound of order d−7 Our method for computing terms in the expansion also applies to percolation, and for nearest-neighbour independent Bernoulli bond percolation on ℤd gives the 1/d-expansion for the critical point through order d−3, with a rigorous error bound of order d−4 The method uses the lace expansion.

Original languageEnglish
Pages (from-to)197-215
Number of pages19
JournalCombinatorics, Probability and Computing
Volume4
Issue number3
DOIs
Publication statusPublished - Sep 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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