The Knotting of Equilateral Polygons in R³

Abstract

It was proved in [4] that the knotting probability of a Gaussian random polygon goes to 1 as the length of the polygon goes to infinity. In this paper, we prove the same result for the equilateral random polygons in R 3 . More precisely, if EP n is an equilateral random polygon of n steps, then we have [Formula: see text] provided that n is large enough, where ∊ is some positive constant.