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Gibbs Ensembles of Nonintersecting Paths

Borodin, Alexei and Shlosman, Senya (2010) Gibbs Ensembles of Nonintersecting Paths. Communications in Mathematical Physics, 293 (1). pp. 145-170. ISSN 0010-3616.

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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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Additional Information:© Springer-Verlag 2009. Received: 29 June 2008. Accepted: 14 July 2009. Published online: 30 August 2009. Communicated by H. Spohn.
Issue or Number:1
Record Number:CaltechAUTHORS:20100107-101054765
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17088
Deposited By: Tony Diaz
Deposited On:12 Jan 2010 18:05
Last Modified:03 Oct 2019 01:22

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