Electronic Journal of Probability

Traffic distributions of random band matrices

Benson Au

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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

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

Received: 3 December 2017
Accepted: 25 July 2018
First available in Project Euclid: 12 September 2018

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Zentralblatt MATH identifier

Primary: 15B52: Random matrices 46L53: Noncommutative probability and statistics 46L54: Free probability and free operator algebras 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

free probability random band matrix traffic probability Wigner matrix

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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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