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Creators/Authors contains: "Hurley, Jackson"

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  1. ; ; (, Canadian Mathematical Bulletin)
    Abstract We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to extend the main theorem in Chávez, Garcia, and Hurley (2023,Canadian Mathematical Bulletin66, 808–826) from exponent$$d\geq 2$$to$$d \geq 1$$. Our proofs are much simpler than the originals: they do not require Lewis’ framework for group invariance in convex matrix analysis. This clarification puts the entire theory on simpler foundations while extending its range of applicability. 
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  2. ; ; (, Canadian Mathematical Bulletin)
    Abstract We introduce a family of norms on the$$n \times n$$complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in noncommuting variables. As a consequence, we obtain a generalization of Hunter’s positivity theorem for the complete homogeneous symmetric polynomials. 
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