Anisotropic growth of random surfaces in \({2+1}\) dimensions
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.
scientific article; zbMATH DE number 6249793
scientific article