A generalised inductive approach to the lace expansion

Details A generalised inductive approach to the lace expansion A generalised inductive approach to the lace expansion

2000-12-05

arxiv.org/abs/math/0012026v1

Mathematics

Probability

37 pages, in AMS-LaTex

Scientific paper

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

Affiliated with

Also associated with

No associations

Rating

A generalised inductive approach to the lace expansion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A generalised inductive approach to the lace expansion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A generalised inductive approach to the lace expansion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-31079