3 research outputs found
Genus expansion for real Wishart matrices
We present an exact formula for moments and cumulants of several real
compound Wishart matrices in terms of an Euler characteristic expansion,
similar to the genus expansion for complex random matrices. We consider their
asymptotic values in the large matrix limit: as in a genus expansion, the terms
which survive in the large matrix limit are those with the greatest Euler
characteristic, that is, either spheres or collections of spheres. This
topological construction motivates an algebraic expression for the moments and
cumulants in terms of the symmetric group. We examine the combinatorial
properties distinguishing the leading order terms. By considering higher
cumulants, we give a central limit-type theorem for the asymptotic distribution
around the expected value