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

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

2009-04-16

arxiv.org/abs/0904.2607v2

Communications on Pure and Applied Mathematics, Volume 63, Issue 7, pages 831-894, July 2010

Mathematics

Representation Theory

60 pages, corrected proof of theorem 5.2 (results unchanged), updated references

Scientific paper

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.

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