### LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES

Götze F, Naumov AA, Tikhomirov AN (2015)
THEORY OF PROBABILITY AND ITS APPLICATIONS 59(1): 23-39.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Götze, FriedrichUniBi; Naumov, A. A.; Tikhomirov, A. N.
Einrichtung
Abstract / Bemerkung
In this paper we study random symmetric matrices with dependent entries. Suppose that all entries have zero mean and finite variances, which can be different. Assuming that the average of normalized sums of variances in each row converges to one and the Lindeberg condition holds true, we prove that the empirical spectral distribution of eigenvalues converges to Wigner's semicircle law. The result can be generalized to the class of covariance matrices with dependent entries. In this case expected empirical spectral distribution function converges to the Marchenko-Pastur law.
Stichworte
random matrices; semicircle law; Marchenko-Pastur law; Catalan numbers
Erscheinungsjahr
2015
Zeitschriftentitel
THEORY OF PROBABILITY AND ITS APPLICATIONS
Band
59
Ausgabe
1
Seite(n)
23-39
ISSN
0040-585X
eISSN
1095-7219
Page URI
https://pub.uni-bielefeld.de/record/2917110

### Zitieren

Götze F, Naumov AA, Tikhomirov AN. LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES. THEORY OF PROBABILITY AND ITS APPLICATIONS. 2015;59(1):23-39.
Götze, F., Naumov, A. A., & Tikhomirov, A. N. (2015). LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES. THEORY OF PROBABILITY AND ITS APPLICATIONS, 59(1), 23-39. doi:10.1137/S0040585X97986916
Götze, F., Naumov, A. A., and Tikhomirov, A. N. (2015). LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES. THEORY OF PROBABILITY AND ITS APPLICATIONS 59, 23-39.
Götze, F., Naumov, A.A., & Tikhomirov, A.N., 2015. LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES. THEORY OF PROBABILITY AND ITS APPLICATIONS, 59(1), p 23-39.
F. Götze, A.A. Naumov, and A.N. Tikhomirov, “LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES”, THEORY OF PROBABILITY AND ITS APPLICATIONS, vol. 59, 2015, pp. 23-39.
Götze, F., Naumov, A.A., Tikhomirov, A.N.: LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES. THEORY OF PROBABILITY AND ITS APPLICATIONS. 59, 23-39 (2015).
Götze, Friedrich, Naumov, A. A., and Tikhomirov, A. N. “LIMIT THEOREMS FOR TWO CLASSES OF RANDOM MATRICES WITH DEPENDENT ENTRIES”. THEORY OF PROBABILITY AND ITS APPLICATIONS 59.1 (2015): 23-39.

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