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We consider a Markov evolution of lozenge tilings of a quarter-plane andstudy its asymptotics at large times. One of the boundary rays serves as areflecting wall.  We observe frozen and liquid regions, prove convergence of the localcorrelations to translation-invariant Gibbs measures in the liquid region, andobtain new discrete Jacobi and symmetric Pearcey determinantal point processesnear the wall.  The model can be viewed as the one-parameter family of Plancherel measuresfor the infinite-dimensional orthogonal group, and we use this interpretationto derive the determinantal formula for the correlation functions at any finitetime moment.

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