On Random Knots

Authors

Nicholas Pippenger, Harvey Mudd CollegeFollow
Yuanan Diao, Kensaw State College
De Witt Sumners, Florida State University

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1994

Abstract

In this paper, we consider knotting of Gaussian random polygons in 3-space. A Gaussian random polygon is a piecewise linear circle with n edges in which the length of the edges follows a Gaussian distribution. We prove a continuum version of Kesten's Pattern Theorem for these polygons, and use this to prove that the probability that a Gaussian random polygon of n edges in 3-space is knotted tends to one exponentially rapidly as n tends to infinity. We study the properties of Gaussian random knots, and prove that the entanglement complexity of Gaussian random knots gets arbitrarily large as n tends to infinity. We also prove that almost all Gaussian random knots are chiral.

Rights Information

© World Scientific Publishing Company

Recommended Citation

Diao, Y., Pippenger, N., & Sumners, D.W. (1994). On random knots. Journal of Knot Theory and Its Ramifications, 3(3), 419-429.