Random Surface Growth with a Wall and Plancherel Measures for O(∞)

We consider a Markov evolution of lozenge filings 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 con-elation functions at any finite-time moment. (C) 2010 Wiley Periodicals, Inc.