Abstract
We first derive concentration inequalities based on the logarithmic Sobolev inequality and then give some generic and classical examples of laws that satisfy this inequality. Since we shall use it in these notes for Wigner’s matrices, we focus first on concentration for laws in RN. We then briefly generalize the results to compact Riemannian manifolds in order to state concentration inequalities for probability measures on the orthogonal or unitary group.
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© 2009 Springer-Verlag Berlin Heidelberg
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Guionnet, A. (2009). Concentration inequalities and logarithmic Sobolev inequalities. In: Large Random Matrices: Lectures on Macroscopic Asymptotics. Lecture Notes in Mathematics(), vol 1957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69897-5_5
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DOI: https://doi.org/10.1007/978-3-540-69897-5_5
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69896-8
Online ISBN: 978-3-540-69897-5
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