Determinantal random point fields

Determinantal random point fields are measures on spaces of configurations whose correlation functions have determinantal form. Such measures appear in a wide variety of problems, e.g., that of the distribution of spanning trees in an infinite graph, of eigenvalues of random matrices, of zeros of a random analytic function, of the first row of a Plancherel Young diagram.
The talk, aimed at a wide mathematical audience, will give an elementary survey of the theory of determinantal processes, concentrated on examples coming from representations of infinite-dimensional groups.