Titlebook: High Dimensional Probability VIII; The Oaxaca Volume Nathael Gozlan,Rafał Latała,Mokshay Madiman Conference proceedings 2019 Springer Natur

魔鬼在游行

Generalized Semimodularity: Order Statistics,r, stating that every generalized .-semimodular function on the .th Cartesian power of a distributive lattice is generalized .-semimodular, may be considered a multi/infinite-dimensional analogue of the well-known Muirhead lemma in the theory of Schur majorization. This result is also similar to a d

倔强一点

Geometry of ,: Classical Results and Recent Developments,m. We also present some more recent developments including a central limit theorem and a large deviations principle for the .-norm of a random point in .. We discuss their relation to the classical results and give hints to various extensions that are available in the existing literature.

间谍活动

Universality of Limiting Spectral Distribution Under Projective Criteria,s. For a class of generalized martingales we show that the asymptotic behavior of the empirical spectral distribution depends only on the covariance structure. Applications are given to strongly mixing random fields. The technique is based on a blend of blocking procedure, martingale techniques and

最高点

Spongy-Bone

Concentration Inequalities for Randomly Permuted Sums, uniformly permuted sums have been largely studied in the literature. Recently, Delyon et al. proved a new Bernstein-type concentration inequality based on martingale theory. This work presents a new proof of this inequality based on the fundamental inequalities for random permutations of Talagrand.

HALL

Uncertainty Quantification for Matrix Compressed Sensing and Quantum Tomography Problems,e are employed to devise adaptive sequential sampling procedures that guarantee recovery of the true matrix in Frobenius norm after a data-driven stopping time . for the number of measurements that have to be taken. With high probability, this stopping time is minimax optimal. We detail applications

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大方一点

Moment Estimation Implied by the Bobkov-Ledoux Inequality,s close to the question posted by Adamczak and Wolff in (Probab Theory Related Fields 162:531–586, 2015) regarding moments estimate for locally Lipschitz functions, which is expected to result from B-L inequality.

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Universality of Limiting Spectral Distribution Under Projective Criteria, second part of the paper contains a survey of several old and new asymptotic results for the empirical spectral distribution for Gaussian processes, which can be combined with our universality results.

phlegm

Exchangeable Pairs on Wiener Chaos,of Brownian motions and we discover a natural link between Malliavin operators and these exchangeable pairs. By combining our findings with E. Meckes’ infinitesimal version of exchangeable pairs, we can give another proof of the quantitative fourth moment theorem. Finally, we extend our result to the multidimensional case.