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We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements...
For fixed m > 1, we consider m independent n×n non-Hermitian random matrices X1, . . . ,Xm with i.i.d. centered entries with a finite (2 + )-th moment,  > 0. As n tends to infinity, we show that the...
We consider products of independent random matrices with independent entries.The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let X()jk , 1 ≤...
We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is com...
Let {Mi}ℓ i=1 be a non-trivial family of d × d complex matrices, in the sense that for any n ∈ N, there exists i1 · · · in ∈ {1, . . . , ℓ}n such that Mi1 · · ·Min 6= 0. Let P: (0,∞) → R b...

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