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

نویسندگان

  • Takashi Hara
  • Gordon Slade
چکیده

We prove existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on Z d . For the critical point, de ned to be the reciprocal of the connective constant, the coe cients 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 Z d 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.

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عنوان ژورنال:
  • Combinatorics, Probability & Computing

دوره 4  شماره 

صفحات  -

تاریخ انتشار 1995