Fluctuations of the Occupation Density for a Parking Process

ABSTRACT: Consider the following simple parking process on n := {−n,..., n}d , d ≥ 1: at each step, a site i is chosen at random in n and if i and all its nearest neighbor sites are empty, i is occupied. Once occupied, a site remains so forever. The process continues until all sites in n are either occupied or have at least one of their nearest neighbors occupied. The final configuration (occupancy) of n is called the jamming limit and is denoted by Xn . Ritchie (J Stat Phys 122:381–398, 2006) constructed a stationary random field on Zd obtained as a (thermodynamic) limit of the Xn ’s as n tends to infinity. As a consequence of his construction, he proved a strong law of large numbers for the proportion of occupied sites in the box n for the random field X. Here we prove the central limit theorem, the law of iterated logarithm, and a gaussian concentration inequality for the same statistics. A particular attention will be given to the case d = 1, in which we also obtain new asymptotic properties for the sequence Xn , n ≥ 1.

• Autores: Roldán Correa, Alejandro; Valencia Henao, León Alexander; Gallo, Sandro; Coletti, Cristian F.
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2024
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/43221
• Acceso en línea: https://hdl.handle.net/10495/43221
• Palabra clave: Teorema del límite central; Central limit theorem; Distribución asintótica (teoría de probabilidades); Asymptotic distribution (probability theory); Parking process; Jamming limit; Thermodynamic limit; Random sequential adsorption; Concentration inequalities
• Rights: openAccess
• License: http://creativecommons.org/licenses/by/2.5/co/