We consider planar first-passage percolation and show that the time constant can be bounded by multiples of the first and second tertiles of the weight distribution. As a consequence, we obtain a counter-example to a problem proposed by Alm and Deijfen (2015).

中文翻译：

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三分位数和时间常数

我们考虑平面第一通道渗透并表明时间常数可以由权重分布的第一和第二三分位数的倍数限制。因此，我们获得了 Alm 和 Deijfen (2015) 提出的问题的反例。