Genus Expansion for Real Wishart Matrices

C. Emily I. Redelmeier ()
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C. Emily I. Redelmeier: Queen’s University

Journal of Theoretical Probability, 2011, vol. 24, issue 4, 1044-1062

Abstract: Abstract 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.

Keywords: Real Wishart matrices; Genus expansion; Maps on non-orientable surfaces; Central limit theorem; 15A52; 60G15; 05A15 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-010-0278-7

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