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| HAL : hal-00002167, version 1 |
| arXiv : math.PR/0407021 |
| Fiche détaillée |  Récupérer au format |
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| combinatorics Probability & computing 16 (2007) 417-434 |
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| Limit law of the standard right factor of a random Lyndon word |
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| Regine Marchand 1Elahe Zohoorian Azad 1 |
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| (23/01/2007) |
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| Consider the set of finite words on a totally ordered alphabet with $q$ letters. We prove that the distribution of the length of the standard right factor of a random Lyndon word with length $n$, divided by $n$, converges to: $$\mu(dx)=\frac1q \delta_{1}(dx) + \frac{q-1}q \mathbf{1}_{[0,1)}(x)dx,$$ when $n$ goes to infinity. The convergence of all moments follows. This paper completes thus the results of~\cite{Bassino}, giving the asymptotics of the mean length of the standard right factor of a random Lyndon word with length $n$ in the case of a two letters alphabet. |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| Domaine | : | Mathématiques/Probabilités |
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| hal-00002167, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00002167 | |
| oai:hal.archives-ouvertes.fr:hal-00002167 | |
| Contributeur : Regine Marchand | |
| Soumis le : Jeudi 1 Juillet 2004, 20:05:00 | |
| Dernière modification le : Mardi 29 Mai 2007, 15:45:45 | |
