An Analysis upon Some Properties of Determinantal Point Processes and Zeros of Certain Gaussian Analytic Functions | Original Article
Random configurations of points in space, also known as point processes, have been studied in mathematics, statistics and physics for many decades. In mathematics and statistics, the emphasis has been on the Poisson process, which can be thought of as a limit of picking points independently and uniformly in a large region. Taking a different perspective, a finite collection of points in the plane can always be considered as the roots of a polynomial; in this coordinate system, taking the coefficients of the polynomial to be independent is natural. Limits of these random polynomials and their zeros are a core subject of this study; the other class consists of processes with joint intensities of Determinantal form.