| |
Record |
Links |
|
Author  |
Barrera, J.; Fontbona, J. |
|
| |
Title |
The Limiting Move-To-Front Search-Cost In Law Of Large Numbers Asymptotic Regimes |
Type |
|
| |
Year |
2010 |
Publication |
Annals Of Applied Probability |
Abbreviated Journal |
Ann. Appl. Probab. |
|
| |
Volume |
20 |
Issue |
2 |
Pages |
722-752 |
|
| |
Keywords |
Move-to-front rule; search-cost; law of large numbers; propagation of chaos |
|
| |
Abstract |
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. |
|
| |
Address |
[Barrera, Javiera] Univ Adolfo Ibanez, Escuela Ingn & Ciencias, Penalolen, Chile, Email: javiera.barrera@uai.cl |
|
| |
Corporate Author |
|
Thesis |
|
|
| |
Publisher |
Inst Mathematical Statistics |
Place of Publication |
|
Editor |
|
|
| |
Language |
English |
Summary Language |
|
Original Title |
|
|
| |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
|
| |
Series Volume |
|
Series Issue |
|
Edition |
|
|
| |
ISSN |
1050-5164 |
ISBN |
|
Medium |
|
|
| |
Area |
|
Expedition |
|
Conference |
|
|
| |
Notes |
WOS:000283529500012 |
Approved |
|
|
| |
Call Number |
UAI @ eduardo.moreno @ |
Serial |
101 |
|
| Permanent link to this record |
