We present a brief survey of fluctuations and large deviations of particle systems with
subextensive growth of the variance. These are called hyperuniform (or …

We study translation invariant stochastic processes on R^ d R d or Z^ d Z d whose diffraction
spectrum or structure function S (k), ie the Fourier transform of the truncated total pair …

We consider particle systems (also known as point processes) on the line and in the plane
and are particularly interested in “hole” events, when there are no particles in a large disk (or …

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 …

For a broad class of point processes, including determinantal point processes, we construct
associated marked and conditional ensembles, which allow to study a random configuration …

Stochastic point processes with Coulomb interactions arise in various natural examples of
statistical mechanics, random matrices and optimization problems. Often such systems due …

In certain point processes, the configuration of points outside a bounded domain
determines, with probability 1, certain statistical features of the points within the domain. This …

We develop a technique for proving number rigidity (in the sense of Ghosh and Peres in
Duke Math J 166 (10): 1789–1858, 2017) of the spectrum of general random Schrödinger …

We introduce and study a notion of duality for two classes of optimization problems
commonly occurring in probability theory. That is, on an abstract measurable space (Ω, F) …

A problem of fundamental interest in mathematical physics is that of understanding the
structure of the spectrum of random Schrödinger operators. An important tool in such …