Electronic Communications in Probability

On the spectral properties of a class of $H$-selfadjoint random matrices and the underlying combinatorics

Michal Wojtylak and Patryk Pagacz

Full-text: Open access

Abstract

An expansion of the Weyl function of a $H$-selfadjoint random matrix with one negative square is provided. It is shown that the coefficients converge to a certain generalization of Catlan numbers. Properties of this generalization are studied, in particular, a combinatorial interpretation is given.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 7, 14 pp.

Dates
Accepted: 7 February 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316709

Digital Object Identifier
doi:10.1214/ECP.v19-3066

Mathematical Reviews number (MathSciNet)
MR3167880

Zentralblatt MATH identifier
1297.15039

Subjects
Primary: 15B52: Random matrices
Secondary: 15B57: Hermitian, skew-Hermitian, and related matrices 05A19: Combinatorial identities, bijective combinatorics

Keywords
Wigner matrix $H$-selfadjoint matrix eigenvalue of nonpositive type Catalan numbers

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Wojtylak, Michal; Pagacz, Patryk. On the spectral properties of a class of $H$-selfadjoint random matrices and the underlying combinatorics. Electron. Commun. Probab. 19 (2014), paper no. 7, 14 pp. doi:10.1214/ECP.v19-3066. https://projecteuclid.org/euclid.ecp/1465316709


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