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Teoriya Veroyatnostei i ee Primeneniya, 2013, Volume 58, Issue 2, Pages 401–410
DOI: https://doi.org/10.4213/tvp4515 (Mi tvp4515) 		 
Short Communications

Concentration inequalities for smooth random fields

D. V. Belomestnya, V. G. Spokoinyb

a University of Duisburg-Essen
b Weierstrass-Institut für Angewandte Analysis und Stochastik, Berlin
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DOI: https://doi.org/10.4213/tvp4515
Abstract: In this paper we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some deterministic point plus an intrinsic dimension of the optimization problem. As an application we prove the exponential inequality for a function of the maximal eigenvalue of a random matrix.
Keywords: smooth random fields; concentration inequalities; maximal eigenvalue of a random matrix.
Received: 19.03.2013
English version:
Theory of Probability and its Applications, 2014, Volume 58, Issue 2, Pages 314–323
DOI: https://doi.org/10.1137/S0040585X9798659X
Bibliographic databases:
Document Type: Article
MSC: 60
Language: English
Citation: D. V. Belomestny, V. G. Spokoiny, “Concentration inequalities for smooth random fields”, Teor. Veroyatnost. i Primenen., 58:2 (2013), 401–410; Theory Probab. Appl., 58:2 (2014), 314–323
Citation in format AMSBIB
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