Construction of the Thermodynamic Jamming Limit for the Parking Process and Other Exclusion Schemes on Z^d

The Jamming Constant of Uniform Random Graphs

By constructing jointly a random graph and an associated exploration process, we define the dynamics of a "parking process" on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree distribution of non-explored nodes. We then establish a functional law of large numbers for this process as the number of vertices grows to infinity, allowing us to assess the jamming constant of the considered random graphs, i.e. the size of the maximal independent set discovered by the exploration algorithm. This technique, which can be applied to any uniform random…

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

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。

Renyi's Parking Problem Revisited

Rényi's parking problem (or $1D$ sequential interval packing problem) dates back to 1958, when Rényi studied the following random process: Consider an interval $I$ of length $x$, and sequentially and randomly pack disjoint unit intervals in $I$ until the remaining space prevents placing any new segment. The expected value of the measure of the covered part of $I$ is $M(x)$, so that the ratio $M(x)/x$ is the expected filling density of the random process. Following recent work by Gargano {\it et al.} \cite{GWML(2005)}, we studied the discretized version of the above process by considering the p…

停车过程占据密度的涨落

Fluctuations of the occupation density for a parking process

本文研究随机停车过程阻塞极限中占据位点比例的涨落，证明了中心极限定理、重对数律和高斯集中不等式，并在一维情形给出新渐近性质及密度闭式公式的新证明。