Divergence of shape fluctuations in two dimensions
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.
scientific article; zbMATH DE number 823392
scientific article