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2018 Limiting behaviour of the stationary search cost distribution driven by a generalized gamma process
Alfred Kume, Fabrizio Leisen, Antonio Lijoiï
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP111


Consider a list of labeled objects that are organized in a heap. At each time, object $j$ is selected with probability $p_j$ and moved to the top of the heap. This procedure defines a Markov chain on the set of permutations which is referred to in the literature as Move-to-Front rule. The present contribution focuses on the stationary search cost, namely the position of the requested item in the heap when the Markov chain is in equilibrium. We consider the scenario where the number of objects is infinite and the probabilities $p_j$’s are defined as the normalization of the increments of a subordinator. In this setting, we provide an exact formula for the moments of any order of the stationary search cost distribution. We illustrate the new findings in the case of a generalized gamma subordinator and deal with an extension to the two–parameter Poisson–Dirichlet process, also known as Pitman–Yor process.


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Alfred Kume. Fabrizio Leisen. Antonio Lijoiï. "Limiting behaviour of the stationary search cost distribution driven by a generalized gamma process." Electron. Commun. Probab. 23 1 - 10, 2018.


Received: 11 April 2017; Accepted: 25 January 2018; Published: 2018
First available in Project Euclid: 23 February 2018

zbMATH: 1390.60181
MathSciNet: MR3771769
Digital Object Identifier: 10.1214/18-ECP111

Primary: 60G57
Secondary: 60G51

Keywords: $\gamma $–stable process , generalized gamma process , heaps , move-to-front rule, search cost distribution , subordinator , two–parameter Poisson–Dirichlet process


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