均匀停车过程的精确有限长度理论：空间规律、吸收与聚集
Exact Finite-Length Theory of Uniform Car Parking: Spatial Laws, Absorption, and Aggregation
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中文总结 AI 辅助
本文针对均匀停车过程的有限长度$s$，提出精确理论，将停放位置联合密度分解为阻塞单元并以子集递归计算，通过超对数获取边缘分布与间隙统计，借助Rényi积分方程处理吸收计数与聚集量。
中文摘要 AI 辅助
均匀停车过程是在长度为$s$的有限线段上对单位车辆进行的一维随机顺序吸附：车辆以均匀随机位置到达，只要有空间就停放，直到没有间隙能容纳另一辆车为止。本文发展了精确的有限$s$理论。停放位置的联合密度被分解为阻塞单元，每个单元上它是一个有理函数，并通过子集递归以$O(2^n n)$的运算量计算；边缘分布和间隙顺序统计量作为超对数得到，其权重由积分掉的坐标数量确定；吸收计数与聚集量通过源自Rényi的积分方程处理。
英文摘要
The uniform car-parking process is the one-dimensional random sequential adsorption of unit cars on a segment of finite length $s$: cars arrive at uniformly random positions and park wherever they fit, until no gap admits another. This paper develops the exact finite-$s$ theory. The joint density of the parked positions is resolved into jamming cells, on each of which it is a rational function, and evaluated by a subset recursion in $O(2^n n)$ operations; the marginal and gap order statistics are obtained as hyperlogarithms whose weight is fixed by the number of coordinates integrated out; and the absorption count and the aggregate quantities are treated through the integral equation descending from Rényi.
