scholarly journals Combinatorial random knots

2020 ◽  
Vol 13 (4) ◽  
pp. 633-654
Author(s):  
Andrew Ducharme ◽  
Emily Peters
Keyword(s):  
Random Knots

Mean unknotting times of random knots and embeddings

2007 ◽  
Vol 2007 (05) ◽  
pp. P05004-P05004 ◽  
Author(s):  
Yao-ban Chan ◽  
Aleksander L Owczarek ◽  
Andrew Rechnitzer ◽  
Gordon Slade
Keyword(s):  
Random Knots

scholarly journals Invariants of Random Knots and Links

2016 ◽  
Vol 56 (2) ◽  
pp. 274-314 ◽  
Author(s):  
Chaim Even-Zohar ◽  
Joel Hass ◽  
Nati Linial ◽  
Tahl Nowik
Keyword(s):  
Knots And Links ◽  
Random Knots

RANDOM KNOTS AND ENERGY: ELEMENTARY CONSIDERATIONS

1994 ◽  
Vol 03 (03) ◽  
pp. 355-363 ◽  
Author(s):  
GREGORY R. BUCK
Keyword(s):  
Fourier Series ◽  
Piecewise Linear ◽  
Random Knots

We present two constructions of random knots. The first gives piecewise linear knots. It has a parameter (which can be a function), which allows one some control of the expected shape of the knot. The second construction uses Fourier series to construct smooth random knots. We then discuss preliminary notions of the interplay between random knots and the energy of a knot.

scholarly journals Subknots in ideal knots, random knots and knotted proteins

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Eric J. Rawdon ◽  
Kenneth C. Millett ◽  
Andrzej Stasiak
Keyword(s):  
Knotted Proteins ◽  
Random Knots

scholarly journals Scaling behavior of random knots

2003 ◽  
Vol 100 (10) ◽  
pp. 5611-5615 ◽  
Author(s):  
A. Dobay ◽  
J. Dubochet ◽  
K. Millett ◽  
P.-E. Sottas ◽  
A. Stasiak
Keyword(s):  
Scaling Behavior ◽  
Random Knots

scholarly journals Critical Exponents for Random Knots

2000 ◽  
Vol 85 (18) ◽  
pp. 3858-3861 ◽  
Author(s):  
Alexander Yu. Grosberg
Keyword(s):  
Critical Exponents ◽  
Random Knots

ON RANDOM KNOTS

1994 ◽  
Vol 03 (03) ◽  
pp. 419-429 ◽  
Author(s):  
YUANAN DIAO ◽  
NICHOLAS PIPPENGER ◽  
DE WITT SUMNERS
Keyword(s):  
Gaussian Distribution ◽  
Piecewise Linear ◽  
Random Polygon ◽  
Random Polygons ◽  
Almost All ◽  
Random Knots

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.

scholarly journals Models of random knots

2017 ◽  
Vol 1 (2) ◽  
pp. 263-296 ◽  
Author(s):  
Chaim Even-Zohar
Keyword(s):  
Random Knots
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