Convergence of the lace expansion
The lace expansion is a flexible method that has been used since the 1980s to
analyse the critical behaviour of high-dimensional random systems, including
self-avoiding walk, percolation, and spin systems. It originated in work of
Brydges and Spencer on weakly self-avoiding walk in dimensions above 4, and
since then several different approaches have been developed to prove
convergence of the expansion. I will explain what the lace expansion for
self-avoiding walk is, and will then present a new and relatively simple method
for proving convergence of the lace expansion for weakly self-avoiding walk.
The talk is based on a paper to appear in Ann. Inst. H. Poincare Probab.
Statist., available at: link.