Divergence of shape fluctuations in two dimensions
type: Item
instance of: scholarly article
title: Divergence of shape fluctuations in two dimensions
zbMATH Open document ID: 0835.60087
author: Marcelo S. T. Piza
author: Charles M. Newman
published in: The Annals of Probability
publication date: 1996-03-26T00:00:00Z
review text: The authors study some stochastic growth models (mainly three), such as standard first-passage percolation on \(\mathbb{Z}^d\), where to the leading order there is a linearly growing deterministic shape. They prove that for \(d = 2\), the shape fluctuations grow at least logarithmically in all directions. Besides, they also obtain some estimates for the power law.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C24
Mathematics Subject Classification ID: 82B24
Mathematics Subject Classification ID: 82B44
zbMATH DE Number: 823392
zbMATH Keywords: stochastic growth models
zbMATH Keywords: first-passage percolation
zbMATH Keywords: shape fluctuations
reviewed by: Mu-Fa Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988171
OpenAlex ID: W2082512562
DOI: 10.1214/AOP/1176988171
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description: scientific article; zbMATH DE number 823392