Ranking-based rich-get-richer processes

Pantelis Pipergias Analytis, Alexandros Gelastopoulos*, Hrvoje Stojic

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Abstract

We study a discrete-time Markov process X_n in 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 Pólya urns and can be used to study ranking-algorithms for web interfaces.
OriginalsprogEngelsk
TidsskriftAnnals of Applied Probability
ISSN1050-5164
StatusAccepteret/In press - 2022

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