Exact Finite-Length Theory of Uniform Car Parking: Spatial Laws, Absorption, and Aggregation

arXiv:2608.22671v1 Announce Type: new Abstract: 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 Renyi.

Source: arXiv cs.RO | 2026-08-25