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.
Keywords
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}
}
Comments
12 pages