The lace expansion and the enumeration of self-avoiding walks

  • Date: 02/14/2007

Gordon Slade (UBC)


University of British Columbia


The lace expansion is an elegant combinatorial construction that
provides a recursion relation for the number of self-avoiding walks. We
first give an introduction to the lace expansion, and then explain how
it has been used recently (in joint work with Nathan Clisby and Richard
Liang) to enumerate self-avoiding walks on the hypercubic lattice up to
n=30 steps in dimension 3, and up to n=24 steps in all dimensions above
3. Major improvements to the 1/d expansion for the connective constant
have also been obtained. In addition, an algorithmic improvement called
the two-step method will be described.

Other Information: 

Probability Seminar 2007