Concentration Property on Probability Spaces

By Apostolos Giannopoulos, V. Milman. 2000

84 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/92e37d493317d7186bfd819a6aa0e0b563da7e33

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Citations in the corpus

L_p moments of random vectors via majorizing measures (2005, background): “[19, 9] differs from it by the multiplicative coefficient L(2)μ, where Lμ is the isotropic constant of μ (see [19]).”
Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles (2009, background): “Such processes have been studied in [10], [11] and [17].”
On singular values of matrices with independent rows (2006, methodology): “In [7] it was shown that Bourgain’s method can actually give a better estimate of N ≥ c(ε)n log(2) n.”
Uncertainty Principle for Communication Compression in Distributed and Federated Learning and the Search for an Optimal Compressor (2020, unknown): “The concentration of the measure is a remarkable high-dimensional phenomenon which roughly claims that a function deﬁned on a high-dimensional space and having small oscillations takes values highly concentrated around the average (Ledoux, 2001; Giannopoulos & Milman, 2000).”
Introduction to the non-asymptotic analysis of random matrices (2010, background): “58 by decoupling and covering is present in [12] and is followed in [32, 2].”
Concentration of mass on convex bodies (2006, background): “One can actually check (see [17]) that this last estimate can be obtained by Bourgain’s argument if we also use Alesker’s concentration inequality.”
Empirical Processes with a Bounded Ψ1 Diameter (2010, background): “[21, 9, 15, 32, 20, 30, 25, 4]), in which the estimate has been improved from the initial N ≥ c(ε, δ)n2 in [21] to the best possible estimate of N ≥ c(ε, δ)n, proved in [1].”