Closed-form expressions are derived for the expected hyperbolic volume of the convex hull of n beta-distributed random points in the d-dimensional unit ball under the Klein model.
Matrix Analysis
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GL-LowPopArt is a Catoni-style two-stage estimator for generalized low-rank trace regression that attains state-of-the-art bounds and nearly instance-wise minimax optimality up to the Hessian condition number.
Optimal O(n^{-1/2}) convergence in trace distance with third moments and O(n^{-1}) in relative entropy with fourth moments for the quantum CLT in m-mode bosonic systems.
Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
Defines matricial order operator spaces and establishes duality between normality and generation properties, with examples including operator systems and Schatten spaces.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
Witness motifs in constrained geometric graphs saturate Weyl bounds on Laplacian perturbations under heavy-tailed noise, with new metrics SC and S3I to distinguish noise-driven spectral effects.
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.
Generalizes Williamson's theorem to real symmetric matrices allowing arbitrary real symplectic eigenvalues, with explicit constructions and perturbation bounds for the class EigSpSm(2n).
The direct exponent in binary quantum state discrimination for correlation detection equals the doubly minimized Petz Renyi mutual information for alpha in (1/2,1), while the strong converse exponent equals the doubly minimized sandwiched version for alpha in (1,infty).
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Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.