The Annals of Applied Probability

The limiting move-to-front search-cost in law of large numbers asymptotic regimes

Javiera Barrera and Joaquín Fontbona

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We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a “law of large numbers for random partitions,” a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one related to the initial ordering of the list. Our results ensure the stability of the limiting search-cost under general perturbations of the request probabilities. We provide the description of the limiting transient behavior in several examples where only the stationary regime is known, and discuss the range of validity of our scaling limit.

Article information

Ann. Appl. Probab., Volume 20, Number 2 (2010), 722-752.

First available in Project Euclid: 9 March 2010

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Zentralblatt MATH identifier

Primary: 60B10: Convergence of probability measures 68W40: Analysis of algorithms [See also 68Q25]
Secondary: 68P10: Searching and sorting

Move-to-front rule search-cost law of large numbers propagation of chaos


Barrera, Javiera; Fontbona, Joaquín. The limiting move-to-front search-cost in law of large numbers asymptotic regimes. Ann. Appl. Probab. 20 (2010), no. 2, 722--752. doi:10.1214/09-AAP635.

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