论文标题
一维随机顺序吸附的大偏差
Large Deviations in One-Dimensional Random Sequential Adsorption
论文作者
论文摘要
在随机的顺序吸附（RSA）中，对象被随机，不可逆转和顺序沉积。试图导致与先前沉积物体重叠的尝试被丢弃。该过程一直持续到系统无法进一步添加的情况下，直到系统达到堵塞状态为止。我们分析了一类晶格RSA型号，当左侧至少$ b $附近的站点未占用时，允许在该细分市场中降落在一个细分市场中。对于最小模型（$ b = 1 $），我们计算职业编号的完整计数统计信息。我们将完整计数统计信息的确定降低为Riccati方程，该方程仅在$ b = 1 $时在分析上可以解决。我们开发了一个扰动过程，原则上，该过程允许一个人连续确定累积物，并计算所有$ b $的职业编号的差异。
In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed state when no further additions are possible. We analyze a class of lattice RSA models in which landing on an empty site in a segment is allowed when at least $b$ neighboring sites on the left and the right are unoccupied. For the minimal model ($b=1$), we compute the full counting statistics of the occupation number. We reduce the determination of the full counting statistics to a Riccati equation that appears analytically solvable only when $b=1$. We develop a perturbation procedure which, in principle, allows one to determine cumulants consecutively, and we compute the variance of the occupation number for all $b$.
