A simple convergence proof for the lace expansion

Gordon Slade

A simple convergence proof for the lace expansion

Probability 2021-03-09 v2 Mathematical Physics math.MP

Authors: Gordon Slade

Abstract

We use the lace expansion to give a simple proof that the critical two-point function for weakly self-avoiding walk on $\mathbb{Z}^d$ has decay $|x|^{-(d-2)}$ in dimensions $d>4$ . The proof uses elementary Fourier analysis and the Riemann--Lebesgue Lemma.

Keywords

self-avoiding walk

Cite

@article{arxiv.2006.11241,
  title  = {A simple convergence proof for the lace expansion},
  author = {Gordon Slade},
  journal= {arXiv preprint arXiv:2006.11241},
  year   = {2021}
}

Comments

An improvement of Section 3 of arXiv:2006.06532v1, which has been divided into two independent papers. 9 pages. Minor changes in this version. To be published in Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistiques

A simple convergence proof for the lace expansion

Abstract

Keywords

Cite

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