Determinantal point process ($R_k(\mathbf{x})=\det [K(x_i,x_j){]}_{i,j=1}^k$)

A point process is determinantal with kernel $K$ relative to a specified reference measure if every correlation function of a point process is the indicated determinant. A rank-$m$ finite-rank projection kernel gives an exactly $m$-point process, whose symmetric joint density is $\det [K(x_i,x_j)]/m!$.