Tridiagonal Random Matrix: Gaussian Fluctuations and Deviations

Deng Zhang ()
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Deng Zhang: Shanghai Jiao Tong University

Journal of Theoretical Probability, 2017, vol. 30, issue 3, 1076-1103

Abstract: Abstract This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrices. Under quite general assumptions, we prove that the traces are approximately normally distributed. A Multi-dimensional central limit theorem is also obtained here. These results have several applications to various physical models and random matrix models, such as the Anderson model, the random birth–death Markov kernel, the random birth–death Q matrix and the $$\beta $$ β -Hermite ensemble. Furthermore, under an independent-and-identically-distributed condition, we also prove the large deviation principle as well as the moderate deviation principle for the traces.

Keywords: Central limit theorem; Moderate deviation; Large deviation; Tridiagonal random matrix; 60B20; 60F05; 60F10 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0683-7

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