Concentration Inequalities for Smooth Random Fields

DOI10.1137/S0040585X9798659XzbMATH Open1316.60074arXiv1307.1565OpenAlexW2963221173MaRDI QIDQ2877886

Denis Belomestny, V. Spokoiny

Publication date: 27 August 2014

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1307.1565

zbMATH Keywords

random matrixmaximal eigenvalueconcentration inequalitiessmooth random fields

Mathematics Subject Classification ID

Random fields (60G60) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

Related Items (3)

Concentration inequalities for log-concave distributions with applications to random surface fluctuations ⋮ Unnamed Item ⋮ Concentration inequalities for functions of Gibbs fields with application to diffraction and random Gibbs measures

This page was built for publication: Concentration Inequalities for Smooth Random Fields