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- W2302014600 abstract "We study the time constant $mu (e_{1})$ in first passage percolation on $mathbb Z^{d}$ as a function of the dimension. We prove that if the passage times have finite mean, $$lim_{dtoinfty}frac{mu({e}_{1})d}{log d} = frac{1}{2a},$$ where $a in [0,infty ]$ is a constant that depends only on the behavior of the distribution of the passage times at $0$. For the same class of distributions, we also prove that the limit shape is not an Euclidean ball, nor a $d$-dimensional cube or diamond, provided that $d$ is large enough." @default.
- W2302014600 created "2016-06-24" @default.
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- W2302014600 date "2016-01-01" @default.
- W2302014600 modified "2023-10-17" @default.
- W2302014600 title "On the time constant of high dimensional first passage percolation" @default.
- W2302014600 doi "https://doi.org/10.1214/16-ejp1" @default.
- W2302014600 hasPublicationYear "2016" @default.
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