Shuta Nakajima
Published 2018-04-25Version 1
We study non-random fluctuation in the first passage percolation on $\mathbb{Z}^d$ and show that it diverges for any dimension. We also prove the divergence of the non-random shape fluctuation, which was conjectured in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation. {\em Probab. Theory. Related. Fields.} 136(2) 298--320, 2006].
Comments: 9 page, 2 figures, an early version of these results appeared in Sections 1.2 and 7 of arXiv:1706.03493
Divergence of shape fluctuation in First Passage Percolation
First passage percolation with long-range correlations and applications to random Schrödinger operators
First passage percolation, local uniqueness for interlacements and capacity of random walk
![QR code for arXiv:1804.09533 [math.PR]](http://oss.arxitics.com/images/favicon.svg)