Gibbs Ensembles of Nonintersecting Paths
  We consider a family of determinantal random point processes on the two-dimensional lattice and prove that members of our family can be interpreted as a kind of Gibbs ensembles of nonintersecting paths. Examples include probability measures on lozenge and domino tilings of the plane, some of which are non-translation-invariant.   The correlation kernels of our processes can be viewed as extensions of the discrete sine kernel, and we show that the Gibbs property is a consequence of simple linear relations satisfied by these kernels. The processes depend on infinitely many parameters, which are closely related to parametrization of totally positive Toeplitz matrices. 
Alexei Borodin and Senya Shlosman