## Electronic Journal of Probability

### Traffic distributions of random band matrices

Benson Au

#### Abstract

We study random band matrices within the framework of traffic probability. As a starting point, we revisit the familiar case of permutation invariant Wigner matrices and compare the situation to the general case in the absence of this invariance. Here, we find a departure from the usual free probabilistic universality of the joint distribution of independent Wigner matrices. We further prove general Markov-type concentration inequalities for the joint traffic distribution. We then extend our analysis to random band matrices and investigate the extent to which the joint traffic distribution of independent copies of these matrices deviates from the Wigner case.

#### Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 77, 48 pp.

Dates
Accepted: 25 July 2018
First available in Project Euclid: 12 September 2018

https://projecteuclid.org/euclid.ejp/1536717736

Digital Object Identifier
doi:10.1214/18-EJP205

Mathematical Reviews number (MathSciNet)
MR3858905

Zentralblatt MATH identifier
06964771

#### Citation

Au, Benson. Traffic distributions of random band matrices. Electron. J. Probab. 23 (2018), paper no. 77, 48 pp. doi:10.1214/18-EJP205. https://projecteuclid.org/euclid.ejp/1536717736

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