Published January 2010
| Submitted
Journal Article
Open
Gibbs Ensembles of Nonintersecting Paths
- Creators
- Borodin, Alexei
- Shlosman, Senya
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.
Additional Information
© Springer-Verlag 2009. Received: 29 June 2008. Accepted: 14 July 2009. Published online: 30 August 2009. Communicated by H. Spohn.Attached Files
Submitted - 0804.0564.pdf
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Additional details
- Eprint ID
- 17088
- Resolver ID
- CaltechAUTHORS:20100107-101054765
- Created
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2010-01-12Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field