Stability estimates in characterization by identically distributed linear statistics

Zinger, A. A.; Januškevičius, Romanas

doi:10.1007/bf00966466

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Step 3 -Equality In Distribution Of Linear Forms1

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2021

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“…The answer is "no" (which is the reason why we require the finiteness of all moments in Theorem D). In deep of work of Linnik [60], [59], [58] continued by Zinger [77], [76], see also [44,Chapter 2], the following question going back to Marcinkiewicz [63] has been investigated. Suppose that for i.i.d.…”

Section: Step 3 -Equality In Distribution Of Linear Formsmentioning

confidence: 99%

Large deviations for random matrices in the orthogonal group and Stiefel manifold with applications to random projections of product distributions

Kabluchko¹,

Prochno²

2021

Preprint

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We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of trace-class operators and are finite on the set of Hilbert-Schmidt operators M satisfying M M * < 1. As an application of those LDPs, we determine the precise large deviation behavior of k-dimensional random projections of highdimensional product distributions using an appropriate interpretation in terms of point processes, also characterizing the space of all possible deviations. The case of uniform distributions on ℓ p -balls, 1 ≤ p ≤ ∞, is then considered and reduced to appropriate product measures. Those applications generalize considerably the recent work [Johnston, Kabluchko, Prochno: Projections of the uniform distribution on the cube -a large deviation perspective, Studia Mathematica (2021+)].

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Section: Step 3 -Equality In Distribution Of Linear Formsmentioning

confidence: 99%