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Ranking-based rich-get-richer processes
- Publication Year :
- 2019
-
Abstract
- We study a discrete-time Markov process $X_n\in\mathbb{R}^d$, 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 give a condition under which the initial state is irrelevant. Finally, we show how our framework can account for ranking-based P\'olya urns and can be used to study ranking-algorithms for web interfaces.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1910.01066
- Document Type :
- Working Paper