Ornstein - Zernike Behaviour and Analyticity of Shapes for Self-Avoiding Walks on $Z^d$

#### D. Ioffe

1998, v.4, №3, 323-350

ABSTRACT

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 $Z^d$ in any dimension $d\geq 2$ and for any supercritical value of the parameter $\beta >\beta_c (d)$. The related geometry of the equi-decay level sets is studied as well.

Keywords: Ornstein - Zernike behaviour,self-avoiding random walk,local limit theorems,renewal relations