Determinantal point process - Wikipedia

Abstraction: Repulsive point process with probability characterized by kernel determinants

Key points:

• Probability of observing points at locations x1,...,xk is proportional to det[K(xi, xj)]; naturally models global negative correlations (repulsion)
• Eigenvalues of GUE (Gaussian Unitary Ensemble) random matrices form a canonical example with Hermite polynomial kernel
• Spanning trees of a finite graph form a determinantal point process; uniform random spanning tree = DPP on edge set
• Poissonized Plancherel measure on Young diagrams (related to longest increasing subsequence of random permutation) uses discrete Bessel kernel
• Supports efficient algorithms for sampling, marginalization, conditioning, and other inference tasks
• Applied in machine learning for diversity-promoting subset selection; in wireless network modeling (Ginibre process)

Connections: Stochastic Processes · Random Matrix Theory · Point Processes

Source: http://en.wikipedia.org/wiki/Determinantal_point_process