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Register a new userDivergence of non-random fluctuation for Euclidean first-passage percolation
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Shuta Nakajima
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The non-random fluctuation is one of the central objects in first passage percolation. It was proved in [Shuta Nakajima. Divergence of non-random fluctuation in First Passage Percolation. {em Electron. Commun. Probab.} 24 (65), 1-13. 2019.] that for a particular asymptotic direction, it diverges in a lattice first passage percolation with an explicit lower bound. In this paper, we discuss the non-random fluctuation in Euclidean first passage percolations and show that it diverges in dimension $dgeq 2$ in this model also. Compared with the result in cite{N19}, the present result is proved for any direction and improves the lower bound.
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