2015/01/20 by Christopher Joyner, Christopher H. Joyner, Joyner, Christopher H. +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1501.04907
29 pages, 2 figures
arxiv created 2015/01/20 · openalex publication_date 2015/01/20 · arxiv updated 2015/01/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space of matrices and analysing the induced random motion of the eigenvalues - an approach which is similar to Dyson's Brownian motion model but with important modifications. In particular, we show our process is described by a Fokker-Planck equation, up to an error margin which vanishes in the limit of large matrix dimension. The stationary solution of which corresponds to the joint probability density function of certain well-known fixed trace Gaussian ensembles.