Local Spectrum of Truncations of Kronecker Products of Haar Distributed Unitary Matrices
نویسنده
چکیده
We address the local spectral behavior of the random matrix Π1U ⊗kΠ2U ⊗k∗Π1, where U is a Haar distributed unitary matrix of size n×n, the factor k is at most c0 logn for a small constant c0 > 0, and Π1,Π2 are arbitrary projections on l n k 2 of ranks proportional to n. We prove that in this setting the k-fold Kronecker product behaves similarly to the well-studied case when k = 1. AMS Subject Classification: 15B52
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