We study the non-random fluctuation in first passage percolation and show that it diverges. We also prove the divergence of non-random shape fluctuation, which was predicted in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation. Probab. Theory. Related. Fields. 136(2) 298–320, 2006].
"Divergence of non-random fluctuation in First Passage Percolation." Electron. Commun. Probab. 24 1 - 13, 2019. https://doi.org/10.1214/19-ECP267