Concentration inequalities for smooth random fields

Denis Belomestny; Vladimir Spokoiny

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arXiv · 1307.1565

Concentration inequalities for smooth random fields

Denis Belomestny·Vladimir Spokoiny

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Abstract

In this note 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 optimisation problem. As an application we prove the exponential inequality for a function of the maximal eigenvalue of a random matrix is proved.

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Denis Belomestny, Vladimir Spokoiny. 2013-07-05. Concentration inequalities for smooth random fields. https://arxiv.org/abs/1307.1565

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