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Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 2, Pages 401–410 (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

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.

DOI: https://doi.org/10.4213/tvp4515

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English version:
Theory of Probability and its Applications, 2014, 58:2, 314–323

Bibliographic databases:

Document Type: Article
MSC: 60
Received: 19.03.2013
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

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