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.
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