Computing Equilibrium Distributions Of Interacting Particles

When particles interact with attractive-repulsive dynamics, which can model birds flocking, space dust, or a variety of other phenomena, they tend to form a nice distribution. Understanding these distributions is an active area of applied analysis that is highly related to the classical concept of equilibrium measures that arises in approximation theory and random matrix theory. In this talk we discuss the numerical computation of such measures via new results on power law kernels applied to orthogonal polynomials that facilitate exploration of regimes where analysis is not yet available.