# Determinantal point processes

Placeholder notes for a version of the point process, with which I am completely unfamiliar, but about which I am incidentally curious.

Tao is wonderful as ever

Wikipedia says

Let $\Lambda$ be a locally compact Polish space and $\mu$ be a Radon measure on $\Lambda$.
Also, consider a measurable function $K:\Lambda^2\rightarrow ℂ. We say that$X$is a *determinantal point process* on$\Lambda$with kernel$K$if it is a simple point process on$\Lambda$with a joint intensity/Factorial_moment_densityorcorrelation function (which is the density of its factorial moment measure) given by $$\rho_n(x_1,\ldots,x_n) = \det[K(x_i,x_j)]_{1 \le i,j \le n}$$ for every$n\ geq 1$and$x_1,\dots, x_n\in \Lambda.\$