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2018 A random walk approach to linear statistics in random tournament ensembles
Christopher H. Joyner, Uzy Smilansky
Electron. J. Probab. 23: 1-37 (2018). DOI: 10.1214/18-EJP199


We investigate the linear statistics of random matrices with purely imaginary Bernoulli entries of the form $H_{pq} = \overline{H} _{qp} = \pm i$, that are either independently distributed or exhibit global correlations imposed by the condition $\sum _{q} H_{pq} = 0$. These are related to ensembles of so-called random tournaments and random regular tournaments respectively. Specifically, we construct a random walk within the space of matrices and show that the induced motion of the first $k$ traces in a Chebyshev basis converges to a suitable Ornstein-Uhlenbeck process. Coupling this with Stein’s method allows us to compute the rate of convergence to a Gaussian distribution in the limit of large matrix dimension.


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Christopher H. Joyner. Uzy Smilansky. "A random walk approach to linear statistics in random tournament ensembles." Electron. J. Probab. 23 1 - 37, 2018.


Received: 6 February 2018; Accepted: 15 July 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 1398.05094
MathSciNet: MR3858908
Digital Object Identifier: 10.1214/18-EJP199

Primary: 05C20‎, 05C80, 05C81, 15B52


Vol.23 • 2018
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