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On the large N limit of matrix integrals over the orthogonal group

Mathematical Physics 2009-11-13 v1 Disordered Systems and Neural Networks High Energy Physics - Theory math.MP

Abstract

We reexamine the large N limit of matrix integrals over the orthogonal group O(N) and their relation with those pertaining to the unitary group U(N). We prove that lim_{N to infty} N^{-2} \int DO exp N tr JO is half the corresponding function in U(N), and a similar relation for lim_{N to infty} \int DO exp N tr(A O B O^t), for A and B both symmetric or both skew symmetric.

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Cite

@article{arxiv.0805.0315,
  title  = {On the large N limit of matrix integrals over the orthogonal group},
  author = {Jean-Bernard Zuber},
  journal= {arXiv preprint arXiv:0805.0315},
  year   = {2009}
}

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12 pages