CONTINUOUS FIRST-PASSAGE PERCOLATION AND CONTINUOUS GREEDY PATHS MODEL: LINEAR GROWTH

• 成果类型: Article
• 署名作者: Gouere, Jean-Baptiste; Marchand, Regine
• 署名单位: Universite de Orleans; Universite de Lorraine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP523
• 发表日期: 2008
• 页码: 2300-2319
• 关键词: shape

摘要

We study a random growth model on R(d) introduced by Deijfen. This is a continuous first-passage percolation model. The growth occurs by means of spherical outbursts with random radii in the infected region. We aim to find conditions on the distribution of the random radii to determine whether the growth of the process is linear or not. To do so, we compare this model with a continuous analogue of the greedy lattice paths model and transpose results for greedy paths from the lattice setting to the continuous setting.