Gibbs Ensembles of Nonintersecting Paths |
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Authors: | Alexei Borodin Senya Shlosman |
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Affiliation: | 1. Department of Mathematics, Caltech, Pasadena, USA 2. IITP, RAS, Moscow, Russia 3. Centre de Physique Theorique, CNRS, Luminy, Marseille, France
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Abstract: | 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. |
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