A random walk approach to linear statistics in random tournament ensembles
Christopher Joyner (Queen Mary University of London, UK)
We investigate the linear statistics of random matrices with purely imaginary Bernoulli entries exhibit global correlations in terms of row sums. These are related to ensembles of so-called random regular tournaments. Specifically, we construct a random walk within the space of these matrices and show 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.