Knot theory and matrix integrals

Details Knot theory and matrix integrals Knot theory and matrix integrals

2010-06-09

arxiv.org/abs/1006.1812v2

Physics

Mathematical Physics

chapter of the book Random Matrix Theory, Eds Akemann, Baik and Di Francesco

Scientific paper

The large size limit of matrix integrals with quartic potential may be used to count alternating links and tangles. The removal of redundancies amounts to renormalizations of the potential. This extends into two directions: higher genus and the counting of "virtual" links and tangles; and the counting of "coloured" alternating links and tangles. We discuss the asymptotic behavior of the number of tangles as the number of crossings goes to infinity.

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