Genus Expansion for Real Wishart Matrices |
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Authors: | Email author" target="_blank">C?Emily?I?RedelmeierEmail author |
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Institution: | 1.Department of Mathematics & Statistics,Queen’s University,Kingston,Canada |
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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. |
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Keywords: | |
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