Random knots in three-dimensional three-colour percolation: numerical results and conjectures
Mathematical Physics
2019-05-21 v2 Statistical Mechanics
math.MP
Probability
Abstract
Three-dimensional three-colour percolation on a lattice made of tetrahedra is a direct generalization of two-dimensional two-colour percolation on the triangular lattice. The interfaces between one-colour clusters are made of bicolour surfaces and tricolour non-intersecting and non-self-intersecting curves. Because of the three-dimensional space, these curves describe knots and links. The present paper presents a construction of such random knots using particular boundary conditions and a numerical study of some invariants of the knots. The results are sources of precise conjectures about the limit law of the Alexander polynomial of the random knots.
Keywords
Cite
@article{arxiv.1811.09066,
title = {Random knots in three-dimensional three-colour percolation: numerical results and conjectures},
author = {Marthe de Crouy-Chanel and Damien Simon},
journal= {arXiv preprint arXiv:1811.09066},
year = {2019}
}
Comments
minor corrections in the text since v1