The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in \(d \geqslant 2\) dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on \(\mathbb {Z}^{d}\) with parameter p ∈ (0,1]. For each occupied site v, and for each of the 2d possible coordinate directions, declare the entire line segment from v to the next occupied site in the given direction to be either blue or not blue according to a given stochastic rule. In the ‘one-choice model’, each occupied site declares one of its 2d incident segments to be blue. In the ‘independent model’, the states of different line segments are independent.

对于\（d \ geqslant 2 \）维中相交的线段的两个随机模型，探讨了无限簇的存在与否。在每种情况下都建立了相图的显着特征。该模型是基于点渗流上\（\ mathbb {Z} ^ {d} \）具有参数p ∈（0,1]。对于每一个占用站点v，并且对于每个2的d可能坐标方向，声明根据给定的随机规则，从v到给定方向上的下一个占用位置的整个线段为蓝色或不为蓝色在“单选模型”中，每个占用位置都声明其2 d之一事件段变为蓝色。在“独立模型”中，不同线段的状态是独立的。