The Knotting of Equilateral Polygons in R-cubed

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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 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.