On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices
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DOI: 10.1007/s00440-021-01101-0
Abstract: Let $U^N = (U_1^N,\dots, U^N_p)$ be a d-tuple of $N\times N$ independent Haar unitary matrices and $Z^{NM}$ be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\otimes \mathbb{M}_M(\mathbb{C})$. Let $P$ be a self-adjoint non-commutative polynomial. In 1998,… read more here.
Keywords: haar unitary; unitary matrices; almost surely; deterministic matrices ... See more keywords
On the Outlying Eigenvalues of a Polynomial in Large Independent Random Matrices
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DOI: 10.1093/imrn/rnz080
Abstract: Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A_N,B_N)$, where $A_N$ and $B_N$ are independent Hermitian random matrices and the distribution of $B_N$… read more here.
Keywords: random matrices; outlying eigenvalues; eigenvalues polynomial; almost surely ... See more keywords