Divergence of non-random fluctuation in First Passage Percolation

Shuta Nakajima

Divergence of non-random fluctuation in First Passage Percolation

Probability 2021-03-26 v3 Mathematical Physics math.MP

Authors: Shuta Nakajima

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].

Keywords

first passage percolation non-random fluctuation divergence shape fluctuation z^d

Cite

@article{arxiv.1804.09533,
  title  = {Divergence of non-random fluctuation in First Passage Percolation},
  author = {Shuta Nakajima},
  journal= {arXiv preprint arXiv:1804.09533},
  year   = {2021}
}

Comments

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

Divergence of non-random fluctuation in First Passage Percolation

Abstract

Keywords

Cite

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