Divergence of shape fluctuation for general distributions in first passage percolation

Abstract

We study the shape fluctuation in the first passage percolation on ${\mathbb{Z}}^d$. It is known that it diverges when the distribution obeys Bernoulli in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation. Probab. Theory. Related. Fields. 136(2) 298-320, 2006]. In this paper, we extend the result to general distributions.

11 pages, 4 figures. title changed. The results for non-random fluctuation has moved to arXiv:1804.09533