The Knotting of Equilateral Polygons in R-cubed
It was proved in  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 R3. More precisely, if EPn is an equilateral random polygon of n steps, then we have
P(EPn is knotted) > 1 - exp(-n∊)
provided that n is large enough, where ∊ is some positive constant.
Diao, Y. (1995). The knotting of equilateral polygons in R-cubed. Journal of Knot Theory and Its Ramifications, 4(2), 189-196. DOI: 10.1142/S0218216595000090