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

A point process is said to be rigid if for any bounded domain in the phase space, the number
of particles in the domain is almost surely determined by the restriction of the configuration to …

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 study determinantal point processes on CC induced by the reproducing kernels of
generalized Fock spaces as well as those on the unit disc DD induced by the reproducing …

We give sufficient conditions for the number rigidity of a large class of point processes in
dimension d= 1 d= 1 and 2, based on the decay of correlations. Number rigidity implies that …

We prove that the tagged particles of infinitely many Brownian particles in R 2 interacting via
a logarithmic (two-dimensional Coulomb) potential with inverse temperature β= 2 are sub …

We establish a general Berry–Esseen type bound which gives optimal bounds in many
situations under suitable moment assumptions. By combining the general bound with Palm …

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 study the mutual regularity properties of Palm measures of point processes, and
establish that a key determining factor for these properties is the rigidity-tolerance behaviour …

Let $\varUpsilon $ be the configuration space over a complete and separable metric base
space, endowed with the Poisson measure $\pi $. We study the geometry of $\varUpsilon …