The scaling limit of self-avoiding random walk in high dimensions (Q1115016)

The Brydges-Spencer lace expansion is used to prove that the scaling limit of the finite-dimensional distributions of self-avoiding random walk in the d-dimensional cubic lattice \({\mathbb{Z}}^ d\) is Gaussian, if d is sufficiently large. It is also shown that the critical exponent \(\gamma\) for the number of self-avoiding walks is equal to 1, if d is sufficiently large.