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Journal Articles Journal of Statistical Physics Year : 2019

Random knots in 3-dimensional 3-colour percolation: numerical results and conjectures

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.
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Dates and versions

hal-02285341 , version 1 (12-09-2019)

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Marthe de Crouy-Chanel, Damien Simon. Random knots in 3-dimensional 3-colour percolation: numerical results and conjectures. Journal of Statistical Physics, 2019, 176 (3), pp.574-590. ⟨10.1007/s10955-019-02312-5⟩. ⟨hal-02285341⟩
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