Divergence of non-random fluctuation in First Passage Percolation

Abstract

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].

13 page, 4 figures, an early version of these results appeared in Sections 1.2 and 7 of arXiv:1706.03493. The proof becomes simpler than the first draft

References in corpus (1)

• Sublinear variance in first-passage percolation for general distributions