Functional summary statistics for point processes on the sphere with an application to determinantal point processes

We study point processes on Sd, the d-dimensional unit sphere Sd, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case d=2. The first part studies reduced Palm distributions and functional summary statistics, including nearest neighbour functions, empty space functions, and Ripley’s and inhomogeneous K-functions. The second part partly discusses the appealing properties of determinantal point process...