Global Knotting in Equilateral Random Polygons

In this paper, we study the knotting probability of equilateral random polygons. It is known that such objects are locally knotted with-probability arbitrarily close to one provided the length is sufficiently large ([4]). For Gaussian random polygons, it has been shown that the probability of global knottedness also tends to one as the length of the polygon tends to infinity [8]. In this paper, we prove that global knotting also occurs in equilateral random polygons with a probability approaching one as the length of the polygons goes to infinity.