Geodesic
Concentration inequalities for smooth random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 401-410

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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. 
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     author = {D. V. Belomestny and V. G. Spokoiny},
     title = {Concentration inequalities for smooth random fields},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {401--410},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a12/}
}
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D. V. Belomestny; V. G. Spokoiny. Concentration inequalities for smooth random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 401-410. http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a12/