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Erschienen in:
Mathematical Foundation Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

4. Concentration of Eigenvalues and Their Functionals

verfasst von : Robert Qiu, Michael Wicks

Erschienen in: Cognitive Networked Sensing and Big Data

Verlag: Springer New York

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Abstract

Chapters 4 and 5 are the core of this book. Talagrand’s concentration inequality is a very powerful tool in probability theory. Lipschitz functions are the mathematics objects. Eigenvalues and their functionals may be shown to be Lipschitz functions so the Talagrand’s framework is sufficient. Concentration inequalities for many complicated random variables are also surveyed here from the latest publications. As a whole, we bring together concentration results that are motivated for future engineering applications.

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Vorheriges Kapitel Concentration of Measure
Nächstes Kapitel Non-asymptotic, Local Theory of Random Matrices
Fußnoten
1
Later we will relax this to “at most 1”.
 
2
The support of a function is the set of points where the function is not zero-valued, or the closure of that set. In probability theory, the support of a probability distribution can be loosely thought of as the closure of the set of possible values of a random variable having that distribution.
 
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Metadaten
Titel
Concentration of Eigenvalues and Their Functionals
verfasst von
Robert Qiu
Michael Wicks
Copyright-Jahr
2014
Verlag
Springer New York
Buch
Cognitive Networked Sensing and Big Data

Print ISBN: 978-1-4614-4543-2

Electronic ISBN: 978-1-4614-4544-9

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-1-4614-4544-9_4

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