Hyperuniform and number rigid stable matchings
vendredi 29 mars 2019, 9h30 - 10h30
We study a stable partial matching of the d-dimensional lattice with a stationary determinantal point process (which includes in particular the Poisson point process) on the d-dimensional Euclidean space with intensity larger than one. The matched points from the determinantal point process form a stationary and ergodic (under lattice shifts) point process with intensity 1 that very much resembles the determinantal point process for intensities close to 1. On the other hand, it is hyperuniform and number rigid, quite in contrast to a Poisson process. We deduce these properties by proving more general results for a stationary point process, whose so-called matching flower (determining the matching partner of a lattice point) has a certain subexponential tail behaviour. For hyperuniformity, we also additionally need to assume some mixing condition on the point process. While there are many examples of hyperuniform or rigid point processes on the plane, there are very few in higher dimensions and our examples yields one such.
This is a joint work with Michael Klatt (Princeton University) and Guenter Last (Karlsruhe Institute of Technology).