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Move-to-front rule is a heuristic updating a list of n items according torequests. Items are required with unknown probabilities (or popularities). Theinduced Markov chain is known to be ergodic. One main problem is the study ofthe 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 extendresults proved by Kingman on the expected stationary search cost. Combiningresults contained in these papers, we obtain the limiting behavior for anymoments of the stationary seach cost as n tends to innity.

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