Major
Physics
Anticipated Graduation Year
2020
Access Type
Open Access
Abstract
Knot theory, a subfield of topology, has surprising applications in biology and quantum mechanics. Mathematical knots are tied within a string fused at its ends instead of letting them remain free. Our new probabilistic approach studies the chances of producing particular knots from the randomization of any knot’s crossings. We show every knot must produce trefoils, the most basic nontrivial knot, and determine what is produced with what probability from three classes of knots. We also conjecture bounds on the probabilities of producing knots with four or fewer crossings.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Random Knots
Knot theory, a subfield of topology, has surprising applications in biology and quantum mechanics. Mathematical knots are tied within a string fused at its ends instead of letting them remain free. Our new probabilistic approach studies the chances of producing particular knots from the randomization of any knot’s crossings. We show every knot must produce trefoils, the most basic nontrivial knot, and determine what is produced with what probability from three classes of knots. We also conjecture bounds on the probabilities of producing knots with four or fewer crossings.