Random surface growth with a wall and Plancherel measures for O(infinity)
Representation Theory
2011-03-08 v2 Mathematical Physics
math.MP
Probability
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.
Cite
@article{arxiv.0904.2607,
title = {Random surface growth with a wall and Plancherel measures for O(infinity)},
author = {Alexei Borodin and Jeffrey Kuan},
journal= {arXiv preprint arXiv:0904.2607},
year = {2011}
}
Comments
60 pages, corrected proof of theorem 5.2 (results unchanged), updated references