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Published July 2010 | public
Journal Article

Random surface growth with a wall and Plancherel measures for O (∞)

Abstract

We consider a Markov evolution of lozenge tilings of a quarter-plane and study its asymptotics at large times. One of the boundary rays serves as a reflecting wall. We observe frozen and liquid regions, prove convergence of the local correlations to translation-invariant Gibbs measures in the liquid region, and obtain new discrete Jacobi and symmetric Pearcey determinantal point processes near the wall. The model can be viewed as the one-parameter family of Plancherel measures for the infinite-dimensional orthogonal group, and we use this interpretation to derive the determinantal formula for the correlation functions at any finite-time moment.

Additional Information

© 2010 Wiley Periodicals, Inc. Received: May 2009. Published Online: 11 Mar 2010. The authors are very grateful to Grigori Olshanski for a number of valuable remarks. The first author (A.B.) was partially supported by National Science Foundation Grant DMS-0707163.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023