科研之友
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摘要
It has been shown recently that the limit moments of W(n) = B(n)B*(n), where B(n) is a product of p independent rectangular random matrices, are certain homogeneous polynomials P-k(d(0),d(1),...,d(p)) in the asymptotic dimensions of these matrices. Using the combinatorics of noncrossing partitions, we explicitly determine these polynomials and show that they are closely related to polynomials which can the moments of rho(t1) boxed times rho(t2) boxed times ... boxed times rho(tm) for any positive t(1),t(2),...,t(m), where boxed times is the free multiplicative convolution in free probability and rho(t) is the Marchenko-Pastur distribution with shape parameter t.
- 出版日期2013-5-31
