Spectral dynamics of interacting particles: in Brownian motion and gravitating dust solutions

Abstract

Statistical analysis of the behaviour of interacting particles suspended in a fluid undergoing Brownian motion is extended by a deeper investigation into its spectral properties. By utilizing random matrix theory, spectral statistics is then integrated into the Einstein–Brownian motion formulation for interacting particles suspended in a fluid. The modified version of the conventional Brownian formulation along with the resulting insights are presented in this work. The second part of this work provides the implementation of spectral statistics to a system of interacting massive particles of a gravitating dust solution. Formulating the system on a Riemannian manifold with a random metric tensor, a deterministic dust solution density is achieved, where spectral and statistical aspects of the relativistic theory of gravity are uncovered. Potential application in modeling properties of galaxy formation and evolution is discussed.