Anisotropic growth of random surfaces in \({2+1}\) dimensions
type: Item
instance of: scholarly article
title: Anisotropic growth of random surfaces in \({2+1}\) dimensions
zbMATH Open document ID: 1303.82015
author: Alexei Borodin
author: Patrik Lino Ferrari
published in: Communications in Mathematical Physics
publication date: 2014-01-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/0804.3035
review text: On the one hand we have random growth of one-dimensional interfaces, and on the other hand we have random surfaces arising from dimers on planar bipartite graphs. These two surfaces exhibit some similarities in their asymptotic properties, and to put this feature clearly in evidence, the authors herein construct a class of two-dimensional random growth models of which different projections provide the surfaces above. The key of the approach is a two-dimensional Markov chain. The geometry of the problem is carefully described, and the asymptotic analysis is carried on by means of correlation functions which have determinantal structure.
Mathematics Subject Classification ID: 82B24
Mathematics Subject Classification ID: 82B41
zbMATH DE Number: 6249793
zbMATH Keywords: random surfaces
zbMATH Keywords: Gaussian fluctuations
zbMATH Keywords: dimers
zbMATH Keywords: bipartite graph
zbMATH Keywords: random growth
reviewed by: Guy Jumarie
MaRDI profile type: Publication
OpenAlex ID: W3099706877
arXiv ID: 0804.3035
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Anisotropic growth of random surfaces in \({2+1}\) dimensions (DOI)
DOI: 10.1007/S00220-013-1823-X