The aim of the talk is to discuss a family of models which are in a certain sense dual to Dyson's circular ensembles.

Recall that Dyson's Circular Unitary Ensemble (CUE) consists of random N-point configurations on the unit circle, where the corresponding probability measure comes from the Haar measure on the compact unitary group U(N).  In the dual picture, we deal with certain random N-point configurations on the 1-dimensional lattice.  The corresponding probability measures P_N can be described as certain discrete orthogonal polynomial ensembles of hypergeometric type.  The measures P_N originated from a representation-theoretic construction (the author's preprint arXiv.org/abs/math/0109193).  Their behavior under a scaling limit transition as N goes to infinity was studied by Borodin and the author (arXiv.org/abs/math/0109194).

In the talk, I shall describe another approach to the measures P_N, based on a direct combinatorial argument.  The advantage of this new approach is that it holds in a wider context (arbitrary values of the "beta parameter" are allowed).