Statistical aspects of determinantal point processes

Determinantal point processes are largely unexplored in statistics, though they possess a number of very attractive properties and have been studied in mathematical physics, combinatorics, and random matrix theory even before the general notion was introduced in Macchi (1975). They have been used to model fermions in quantum mechanics, in classical Ginibre and circular unitary ensembles from random matrix theory, as well as examples arising from non-intersecting random walks and random spanning trees (see Section 4.3 in Hough et al. (2009)). They can be defined on a locally compact space. Hough et al. (2009) provides an excellent survey on the probabilistic aspects of determinantal point processes. The focus in this project is on the statistical aspects for determinantal point processes.