First passage percolation on Z 2 : a simulation study
First passage percolation on Z 2 : a simulation study
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发表时间：
2014
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通讯作者：
Sven Erick Alm;Maria Deijfen
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作者：
Sven Erick Alm;Maria Deijfen
Z2上的第一次扩散是描述正方形格点上的扩散的模型。感染通过最近的邻居站点传播，并且时间动态由附接到边缘的随机通过时间指定。在本文中，增长的速度和形状的感染集的研究，借助大规模的计算机模拟，重点是连续的通过时间分布。发现用于确定指示增长的逆渐近速度的时间常数的值的最重要的量是E（min{τ1，...，τ 4}），其中τ1，.，τ 4是i.i.d.通过时间变量。对于一个大类的通过时间分布的关系是线性的。此外，当从轴向对角线移动时，可以看到方向时间常数增加，因此极限形状包含在半径由沿轴的速度沿着限定的圆中。对于变异性较大的分布，形状更接近圆形。
FirstpassagepercolationonZ 2 isamodelfordescribingthespreadofaninfection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is E(min{τ1 ,...,τ 4}) ,w hereτ1 ,...,τ 4 are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.