The prudent self-avoiding walk in dimension six and higher

Torri Niccolo, Université Paris-Nanterre

The prudent self-avoiding random walk (P-SAW) is a family of self-avoiding walks in which the walk cannot take any step in the direction of a previously visited site, which is an infinite-range repellence condition. The prudent walk was originally introduced as a class of self-avoiding walks which are simple to describe. In the last 20 years this walk has attracted the attention of the combinatorics and probability communities and, until recently, only the dimension d=2 was completely described. In this talk we discuss the behaviour of the uniform P-SAW in high dimension. Our approach is based on the lace-expansion. The talk is based on a joint work with Markus Heydenreich and Lorenzo Taggi.

Area: IS16 - Random walks and disordered models (Niccolò Torri)

Keywords: self-avoiding walks, lace-expansion, random polymers

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