On the Gibbs property for the determinantal point processes

The talk will describe conditional measures in a bounded interval, with respect to fixing the configuration in the exterior, for one-dimensional determinantal point processes governed by integrable kernels.
These conditional measures are given by orthogonal polynomial ensembles with explicitly computed weights. Examples include classical determinantal point processes of random matrix theory such as the sine-process or the process governed by the Bessel kernel. The talk is based on the preprint arXiv:1605.01400.