Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions
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220_2013_Article_1823.pdf
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179073e0c37e83c1111b6a605e832d46
Author(s)
Borodin, Alexei
Ferrari, Patrik L.
Date Issued
November 2013
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
Borodin, Alexei, and Patrik L. Ferrari. “Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions.” Communications in Mathematical Physics 325.2 (2014): 603–684.
Version
Author's final manuscript
Abstract
We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the KPZ class and random tiling models. We show that correlation functions associated to our models have determinantal structure, and we study large time asymptotics for one of the models. The main asymptotic results are: (1) The growing surface has a limit shape that consists of facets interpolated by a curved piece. (2) The one-point fluctuations of the height function in the curved part are asymptotically normal with variance of order ln(t) for time t ≫ 1. (3) There is a map of the (2 + 1)-dimensional space-time to the upper half-plane H such that on space-like submanifolds the multi-point fluctuations of the height function are asymptotically equal to those of the pullback of the Gaussian free (massless) field on H.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00220-013-1823-x
