Pathwise asymptotic behavior of random determinants in the Jacobi ensemble

نویسنده

  • A. Rouault
چکیده

This is a companion paper of [Rou05]. It concentrates on asymptotic properties of determinants of some random matrices in the Jacobi ensemble. Let M ∈ Mn1+n2,r(R) (with r ≤ n1 + n2) be a random matrix whose entries are standard i.i.d. Gaussian. We can decompose MT = (MT 1 ,M T 2 ) with M1 ∈ Mn1,r and M2 ∈ Mn2,r. Then, W1 := MT 1 M1 and W2 := MT 2 M2 are independent r× r Wishart matrices with parameters n1 and n2 and MTM = W1 +W2 is Wishart with parameter n1 + n2. The matrix Z := (W1 +W2)W1(W1 +W2)

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تاریخ انتشار 2008