论文标题
独立随机步行所访问的站点的统计特性
Statistical properties of sites visited by independent random walks
论文作者
论文摘要
一组访问的站点和访问地点的数量是随机行走轨迹的两个基本属性。我们考虑在超立方晶格上进行两次独立的随机步行，并研究与这些特征相关的研究订购概率。首先是在时间间隔（0，t）中的概率，沃克访问的站点数量永远不会超过另一个沃克的地点。第二个是沃克访问的站点仍然是另一个沃克访问的地点的子集的概率。使用数值模拟，我们研究了空间维度中有序概率的主要渐近行为d = 1,2,3,4。我们还研究了访问地点数量之间的关系数量的演变。我们分析地表明，平均纽带数量为$ a_1 \ ln t $，$ a_1 = 0.970508 $在一个维度上，在二维中为$（\ ln t）^2 $。
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice and study ordering probabilities associated with these characteristics. The first is the probability that during the time interval (0,t), the number of sites visited by a walker never exceeds that of another walker. The second is the probability that the sites visited by a walker remain a subset of the sites visited by another walker. Using numerical simulations, we investigate the leading asymptotic behaviors of the ordering probabilities in spatial dimensions d=1,2,3,4. We also study the evolution of the number of ties between the number of visited sites. We show analytically that the average number of ties increases as $a_1\ln t$ with $a_1=0.970508$ in one dimension and as $(\ln t)^2$ in two dimensions.
