WIAS Preprint No. 417, (1998)

Ornstein-Zernike behaviour and analyticity of shapes for self-avoiding walks on Z^d


  • Ioffe, Dmitry

2010 Mathematics Subject Classification

  • 82B41 60K35 82B41


  • Ornstein-Zernike behaviour, self-avoiding random, local limit theorems, renewal relations




We derive precise Ornstein-Zernike asymptotics for the decay of the two-point function in any direction of the simple self-avoiding walk on the integer lattice ℤd in any dimension d ≥ 2 and for any super-critical value of the parameter β ≥ β c (d). The related geometry of the equi-decay level sets is studied as well.

Appeared in

  • Mark. Proc. Rel. Fields, 4 (1998), pp. 323-350

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