Limiting behavior of the search cost distribution for the move-to-front rule in the stable case

Fabrizio Leisen (1) , Antonio Lijoi (2) , Christian Paroissin (3)

1 Faculdad de Ciencias Economicas y Empresariales
2 Dipartimento di Economia Politica
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

Move-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or popularities). The induced Markov chain is known to be ergodic. One main problem is the study of the distribution of the search cost dened as the position of the required item. Here we first establish the link between two recent papers that both extend results proved by Kingman on the expected stationary search cost. Combining results contained in these papers, we obtain the limiting behavior for any moments of the stationary seach cost as n tends to innity.

Mots clés: normalized random measure; random discrete distribution; stable subordinator; problem of heaps

Domaines: Probabilités [math.PR]

Fabrizio Leisen, Antonio Lijoi, Christian Paroissin. Limiting behavior of the search cost distribution for the move-to-front rule in the stable case. 2010. ⟨hal-00496354⟩