The large-Nlimit of matrix integrals over the orthogonal group

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

The large N limit of some matrix integrals over the orthogonal group O(N) and its relation with those pertaining to the unitary group U(N) are reexamined. It is proved that limN→∞ N −2 ∫ DO expN Tr JO is half the corresponding function in U(N), with a similar relation for limN→∞ ∫ DO expN Tr (AOBO), for A and B both symmetric or both skew symmetric. Large N limit of integrals over the orthogona...

Integrals of monomials over the orthogonal group

A recursion formula is derived which allows one to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is expressible as a finite sum of partial fractions in N . The recursion formula largely extends presently available integration formulas for the orthogonal group. © ...

On polynomial integrals over the orthogonal group

We consider integrals of type ∫ On u1 11 . . . u an 1nu b1 21 . . . u bn 2n du, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such integrals, by using combinatorial methods. We present as well a general formula for such integrals, as a sum of products of factorials. Introduction The computation of polynomial integral...

2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.