Hearing random matrices and random waves

Abstract

The eigenangles of random matrices in the three standard circular ensembles are rendered as sounds in several different ways. The different fluctuation properties of these ensembles can be heard, and distinguished from the two extreme cases, of angles that are distributed uniformly round the unit circle and those that are random and uncorrelated. Similarly, in Gaussian random superpositions of monochromatic plane waves in one, two and three dimensions, the dimensions can be distinguished in sounds created from one-dimensional sections.