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Creators/Authors contains: "McSwiggen, Colin"

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  1. ; ; (, Random Structures & Algorithms)
    Free, publicly-accessible full text available September 1, 2026
  2. ; (, Probability Theory and Related Fields)
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  3. ; (, Transactions of the American Mathematical Society)
    This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn’s problem, the randomized Schur’s problem, and the orbital corners process. In this general setting, we prove integral formulae for the probability densities, establish some properties of the densities, and discuss connections to multiplicity problems in representation theory as well as to known results in the symplectic geometry literature. As applications, we show a number of results on marginal problems in quantum information theory and also prove an integral formula for restriction multiplicities. 
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  4. ; (, International Mathematics Research Notices)
    The randomized quantum marginal problem asks about the joint distribution of the partial traces (“marginals”) of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this problem based on studying the mixed moments of the entries of the marginals. For randomized quantum marginal problems that describe systems of distinguishable particles, bosons, or fermions, we prove formulae for these mixed moments, which determine the joint distribution of the marginals completely. Our main tool is Weingarten calculus, which provides a method for computing integrals of polynomial functions with respect to Haar measure on the unitary group. As an application, in the case of two distinguishable particles, we prove some results on the asymptotic behavior of the marginals as the dimension of one or both Hilbert spaces goes to infinity. 
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  5. ; ; (, STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing)
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  6. ; ; (, Communications in Mathematical Physics)
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  7. ; ; (, Journal of Statistical Mechanics: Theory and Experiment)
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  8. (, Communications in Mathematical Physics)
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