Gravitational lensing by eigenvalue distributions of random matrix models

Abstract

We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.

25 pages,11 figures

References in corpus (4)

• Determination of S-curves with applications to the theory of nonhermitian orthogonal polynomials
• Fine structure in the large n limit of the non-hermitian Penner matrix model
• Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies
• Phase space and phase transitions in the Penner matrix model with negative coupling constant