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A new inductive approach to the lace expansion for self-avoiding walks
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  • Published: June 1998

A new inductive approach to the lace expansion for self-avoiding walks

  • Remco van der Hofstad1,
  • Frank den Hollander2 &
  • Gordon Slade1 

Probability Theory and Related Fields volume 111, pages 253–286 (1998)Cite this article

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  • 25 Citations

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Summary.

We introduce a new inductive approach to the lace expansion, and apply it to prove Gaussian behaviour for the weakly self-avoiding walk on ℤd where loops of length m are penalised by a factor e−β/m p (0<β≪1) when: (1) d>4, p≥0; (2) d≤4, . In particular, we derive results first obtained by Brydges and Spencer (and revisited by other authors) for the case d>4, p=0. In addition, we prove a local central limit theorem, with the exception of the case d>4, p=0.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1. e-mail: hofstad@math.mcmaster.ca and slade@mcmaster.ca, , , , , , CA

    Remco van der Hofstad & Gordon Slade

  2. Mathematical Institute, Nijmegen University, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands. e-mail: denholla@sci.kun.nl, , , , , , NL

    Frank den Hollander

Authors
  1. Remco van der Hofstad
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  2. Frank den Hollander
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  3. Gordon Slade
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Received: 29 October 1997 / In revised form: 15 January 1998

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van der Hofstad, R., den Hollander, F. & Slade, G. A new inductive approach to the lace expansion for self-avoiding walks. Probab Theory Relat Fields 111, 253–286 (1998). https://doi.org/10.1007/s004400050168

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  • Issue Date: June 1998

  • DOI: https://doi.org/10.1007/s004400050168

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  • Mathematics Subject Classification: (1991) 82B41
  • 60K35
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