Mathematics

Dirichlet's theorem on diophantine approximation states that for any irrational number a, there are infinitely many rationals  p/q  so that  q|aq-p| < 1.  Erdos-Szusz-Turan asked the question of the probability that this estimate could be improved to  q|aq-p|< A, with q in a fixed range [N, cN], and the behavior of this probability as N grows. We answer their question and provide a wide-ranging generalization to the setti ng of equivariant point processes. This is joint work with Anish Ghosh.