THE KNOTTING OF EQUILATERAL POLYGONS IN R(3)

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 P(EP(n) is knotted) > 1 - exp(-n(epsilon)), provided that n is large enough, where epsilon is some positive constant.