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Quantum Concentration Inequalities [PDF]
Annales Henri Poincaré, 2021 We establish Transportation Cost Inequalities (TCIs) with respect to the quantum Wasserstein distance by introducing quantum extensions of well-known classical methods: First, we generalize the Dobrushin uniqueness condition to prove that Gibbs states of
Giacomo De Palma, C. Rouzé
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Deviation bounds and concentration inequalities for quantum noises [PDF]
Quantum, 2022 We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in terms of the ...
Tristan Benoist +2 more
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Universality and Sharp Matrix Concentration Inequalities [PDF]
Geometric and Functional Analysis, 2022 We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance.
Tatiana Brailovskaya, R. van Handel
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Concentration inequalities for sums of Markov-dependent random matrices [PDF]
Information and Inference A Journal of the IMA, 2023 We give Hoeffding- and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain.
Joe Neeman, Bobby Shi, Rachel A. Ward
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Matrix concentration inequalities and free probability [PDF]
Inventiones Mathematicae, 2021 A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices X = ∑ i g i A i $X=\sum _{i} g_{i} A_{i}$ where g i $g_{i}$ are
A. Bandeira +2 more
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Deviation and concentration inequalities for dynamical systems with subexponential decay of correlations [PDF]
Stochastics and Dynamics, 2022 We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the
C. Cuny, J. Dedecker, F. Merlevède
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Concentration inequalities for ultra log-concave distributions [PDF]
Studia Mathematica, 2021 . We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds.
Heshan Aravinda +2 more
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Random walks on hyperbolic spaces: Concentration inequalities and probabilistic Tits alternative [PDF]
Probability theory and related fields, 2021 The goal of this article is two-fold: in a first part, we prove Azuma–Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space M, we obtain explicit
Richard Aoun, Cagri Sert
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A modified Φ-Sobolev inequality for canonical Lévy processes and its applications
Modern Stochastics: Theory and Applications, 2023 A new modified Φ-Sobolev inequality for canonical ${L^{2}}$-Lévy processes, which are hybrid cases of the Brownian motion and pure jump-Lévy processes, is developed.
Noriyoshi Sakuma, Ryoichi Suzuki
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Multivariate Global-Local Priors for Small Area Estimation
Stats, 2022 It is now widely recognized that small area estimation (SAE) needs to be model-based. Global-local (GL) shrinkage priors for random effects are important in sparse situations where many areas’ level effects do not have a significant impact on the ...
Tamal Ghosh +3 more
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