A generalised inductive approach to the lace expansion

摘要: The lace expansion is a powerful tool for analysing the critical behaviour of self-avoiding walks and percolation. It gives rise to recursion relation which we abstract study using an adaptation inductive method introduced by den Hollander authors. We give conditions under solution behaves as Gaussian, both in Fourier space terms local central limit theorem. These are shown elsewhere hold sufficiently spread-out models networks dimensions d > 4, oriented percolation + 1 5, providing unified approach essential ingredient detailed analysis branching these models.