Large deviations for random matricial moment problems

JOURNAL OF MULTIVARIATE ANALYSIS

卷:106

Article

Gamboa, Fabrice²  Nagel, Jan¹  Rouault, Alain³  Wagener, Jens⁴ 

[1] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany

[2] Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse 9, France

[3] Univ Versailles St Quentin, LMV UMR 8100, F-78035 Versailles, France

[4] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

关键词: Random matrices;    Moment spaces;    Canonical moments;    Large deviations;    Caratheodory functions;    Schur functions;   

DOI  :  10.1016/j.jmva.2011.11.006

来源: Elsevier

【 摘 要 】

We consider the moment space M-n(K) corresponding to p x p complex matrix measures defined on K (K = [0, 1] or K = T). We endow this set with the uniform distribution. We are mainly interested in large deviation principles (LDPs) when n -> infinity. First we fix an integer k and study the vector of the first k components of a random element of M-n(K). We obtain an LDP in the set of k-arrays of p x p matrices. Then we lift a random element of M-n(K) into a random measure and prove an LDP at the level of random measures. We end with an LDP on Caratheodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free