Gibbs ensembles of nonintersecting paths

Alexei Borodin, Senya Shlosman

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We consider a family of determinantal random point processes on the twodimensional 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.

Original languageEnglish
Pages (from-to)145-170
Number of pages26
JournalCommunications in Mathematical Physics
Volume293
Issue number1
DOIs
Publication statusPublished - 2009
Externally publishedYes

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