Point processes

Poisson versus glow worms: who is more random?

Higher dimensional Poisson processes: notes, problems, and an interactive applet

Three good books:

• Poisson processes by Kingman (defines Poisson process on much more general spaces)
• Introduction to random matrices, by Anderson, Guionnet and Zeitouni (The eigenvalues of a random matrix are a point process with repulsion: not Poisson)
• Gaussian analytic functions by Hough, Krishnapur, Peres and Virág (The zeros of a random power series are another point process with repulsion)

Comparison of a 2-dimensional Poisson point process with the zeros of a Gaussian analytic function. Since the zeros repel each another, so they look much more evenly spread out than the Poisson points!

Benedek Valko's course on random matrices. Scroll down for images of the semicircle law (real eigenvalues) and the circular law (complex eigenvalues).