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Pré-Publication, Document De Travail Année : 2019

Random Knots in 3-Dimensional 3-Colour Percolation: Numerical Results and Conjectures

Résumé

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.

Dates et versions

hal-03894601 , version 1 (12-12-2022)

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Marthe de Crouy-Chanel, Damien Simon. Random Knots in 3-Dimensional 3-Colour Percolation: Numerical Results and Conjectures. 2022. ⟨hal-03894601⟩
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