Rigidity of the three-dimensional hierarchical Coulomb gas

Understand

A random set of points in Euclidean space is called `rigid' or `hyperuniform' if the number of points falling inside any given region has significantly smaller fluctuations than the corresponding number for a set of i.i.d.

• random points.
• This phenomenon has received considerable attention in recent years, due to its appearance in random matrix theory, the theory of Coulomb gases and zeros of random analytic functions.
• However, most of the published results are in dimensions one and two.