论文标题
随机顺序覆盖
Random Sequential Covering
论文作者
论文摘要
在随机的顺序覆盖中，相同的对象被随机，不可逆转和顺序沉积。只接受了增加覆盖范围的尝试。有限的系统最终会被拥挤，我们研究了拥挤配置的统计数据。对于通过二聚体覆盖间隔的覆盖，我们确定沉积二聚体的平均数量，计算所有较高的累积物，并确定达到最小和最大拥挤的配置的概率。我们还通过$ \ ell $站点和棍棒的细分市场调查了随机覆盖。覆盖无限的底物将无限期地继续，我们分析了$ \ mathbb {z} $和$ \ mathbb {r}^d $的随机顺序覆盖的动力学。
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested configurations. For the covering of an interval by dimers, we determine the average number of deposited dimers, compute all higher cumulants, and establish the probabilities of reaching minimally and maximally congested configurations. We also investigate random covering by segments with $\ell$ sites and sticks. Covering an infinite substrate continues indefinitely, and we analyze the dynamics of random sequential covering of $\mathbb{Z}$ and $\mathbb{R}^d$.
