Knot theory and matrix integrals
Mathematical Physics
2010-06-14 v2 Combinatorics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1006.1812,
title = {Knot theory and matrix integrals},
author = {P. Zinn-Justin and J. -B. Zuber},
journal= {arXiv preprint arXiv:1006.1812},
year = {2010}
}
Comments
chapter of the book Random Matrix Theory, Eds Akemann, Baik and Di Francesco