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

TL;DR

This paper investigates the large N behavior of matrix integrals over the orthogonal group, revealing their relation to unitary group integrals and establishing specific limiting formulas.

Contribution

It proves that the large N limit of orthogonal group integrals is half of the corresponding unitary group integrals, extending understanding of their asymptotic relations.

Findings

Large N limit of orthogonal group integrals is half of the unitary group case.

Established formulas for integrals involving symmetric or skew-symmetric matrices.

Provided rigorous proofs of the asymptotic relations between orthogonal and unitary integrals.

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.