RANKING-BASED RICH-GET-RICHER PROCESSES

• 成果类型: Article
• 署名作者: Analytis, Pantelis P.; Gelastopoulos, Alexandros; Stojic, Hrvoje
• 署名单位: University of Southern Denmark; Pompeu Fabra University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1921
• 发表日期: 2023
• 页码: 4366-4394
• 关键词: random-walks; exit time; cumulative advantage; models; INEQUALITY; systems; LAW

摘要

We study a discrete-time Markov process X-n is an element of R-d for which the distribution of the future increments depends only on the relative ranking of its components (descending order by value). We endow the process with a rich-get-richer assumption and show that, together with a finite second moments assumption, it is enough to guarantee almost sure convergence of X-n/n. We characterize the possible limits if one is free to choose the initial state and we give a condition under which the initial state is irrelevant. Finally, we show how our framework can account for ranking-based Polya urns and can be used to study ranking algorithms for web interfaces.