A matrix-discrepancy argument proves tight one-way quantum lower bounds for collision finding (Ω(N^{1/4})) and for streaming triangle finding (Ω(√Δ_V)) where Boolean-Hidden-Matching reductions fail.
User-friendly tail bounds for sums of random matrices
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.
representative citing papers
Algorithms achieve almost-linear time for ℓ_p-norm flow and dual regression problems on unit-weighted graphs for a range of p, plus applications to max-flow and total variation.
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citing papers explorer
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Quantum Communication Lower Bounds for Search Problems via Matrix Discrepancy
A matrix-discrepancy argument proves tight one-way quantum lower bounds for collision finding (Ω(N^{1/4})) and for streaming triangle finding (Ω(√Δ_V)) where Boolean-Hidden-Matching reductions fail.
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Flows in Almost Linear Time via Adaptive Preconditioning
Algorithms achieve almost-linear time for ℓ_p-norm flow and dual regression problems on unit-weighted graphs for a range of p, plus applications to max-flow and total variation.
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Statistical Inference for Misspecified Contextual Bandits
Develops IPW-Z estimation framework for misspecified contextual bandits, establishing consistency and asymptotic normality under scaled inverse-propensity convergence for marginal moment targets.