On QMC design sequences generated by determinantal point processes

Abstract: 

The concept of a QMC design sequence was introduced by Brauchart et al (2014). In this talk we give a probabilistic generation of a sequence of QMC designs by using determinantal point processes (DPPs), which are used in a fermion model in quantum mechanics and also studied in probability theory.  We show that spherical ensembles and harmonic ensembles, which are the typical types of DPPs on the sphere, generate QMC design sequences.  Moreover, we introduce DPPs on other regions and related results, if possible.