Limit Distributions for Random Hankel, Toeplitz Matrices and Independent Products
نویسندگان
چکیده
For random selfadjoint (real symmetric, complex Hermitian, or quaternion self-dual) Toeplitz matrices and real symmetric Hankel matrices, the existence of universal limit distributions for eigenvalues and products of several independent matrices is proved. The joint moments are the integral sums related to certain pair partitions. Our method can apply to random Hankel and Toeplitz band matrices, and the similar results are given. In particular, when the band width grows slowly as the dimension N → ∞, the exact limit distribution functions are given (N(0, 1) for Toeplitz band matrices) and some asymptotic commutativity is observed.
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