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
Almost Surely Convergence of the Quantum Entropy of Random Graph States and the Area Law
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DOI: 10.1007/s10773-024-05678-9
Abstract: It is known that the ensemble of random pure quantum states, constructed by bipartite maximally entangled states and random unitary matrices generated according to the Haar measure, exhibits an average entanglement entropy that obeys an… read more here.
Keywords: area law; quantum; almost surely; entropy ... 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
Some Bounds for the Fragmentation Coefficient of Random Graphs
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DOI: 10.3390/axioms14030208
Abstract: Graph fragmentation aims to find the smallest vertex subset whose removal breaks a graph into components of bounded size. While this problem has applications in network dismantling and combinatorics, theoretical bounds on optimal solutions remain… read more here.
Keywords: bounds fragmentation; random; asymptotically almost; almost surely ... See more keywords