一様カーパーキングの厳密な有限長理論：空間法則、吸収、凝集
Exact Finite-Length Theory of Uniform Car Parking: Spatial Laws, Absorption, and Aggregation
有限長の線分上での一様カーパーキング過程（ランダム逐次吸着）について、厳密な有限長理論を展開し、駐車位置の同時密度や統計量を効率的に計算する方法を提案した。
著者: Ganesh P Kumar
分類: cs.RO, cs.DS, cs.SC, math.PR, math.RA
原文アブストラクト
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.