Hyperuniform point processes
- Referent: Günter Last
- Ort: SR 2.059
- Termin: 10.2.2022, 16:00 - 17:30 Uhr
- Gastgeber: Elisa Hartmann
Zusammenfassung
A point process in Euclidean space is said to be hyperuniform, if the variance of the number of points in a large ball grows significantly more slowly than its volume. It turns out that this property is closely related to number rigidity. The latter property means that the number of points inside a given compact set is almost surely determined by the configuration of points outside. Rigidity and hyperuniformity are properties that unify crystals and
exceptional random systems. The local behavior of processes with those properties can very much resemble that of a weakly correlated point process. Only on a global scale a regular geometric pattern might become visible.
In the first part of the talk we provide some examples and discuss a few fundamental properties of hyperuniform
point processes. Then we shall present a new class of hyperuniform point processes introduced and studied
in recent joint work with M. Klatt (Princeton) and D. Yogeshwaran (Bangalore). It arises by a peculiar thinning of a stationary Poisson process (or a more general determinantal point process) based on a stable matching procedure. This thinning is also number rigid.