Random surface growth with a wall and Plancherel measures for <i>O</i> (∞)
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<jats:title>Abstract</jats:title><jats:p>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.</jats:p><jats:p>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.</jats:p><jats:p>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. © 2010 Wiley Periodicals, Inc.</jats:p>
収録刊行物
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- Communications on Pure and Applied Mathematics
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Communications on Pure and Applied Mathematics 63 (7), 831-894, 2010-03-11
Wiley