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Comportement asymptotique des mots aléatoires et des arbres aléatoires, et applications

Abstract : This thesis is divided in two parts. The first part is interested in the probabilistic analysis on words, especially in what concerns Lyndon words. We find in this part the limit law of the length of the standard right factor of random Lyndon words, first in the simple case of the alphabet of two equiprobable letters, then in the case of the finite random words with independent letters pulled of a totally ordered finite or infinite alphabet, according to a general probability distribution. Moreover in this general case, we shall nd the asymptotic joint law of the normalized lengths of the Lyndon factors of a finite word. We finally give in this part, a look on the structure of Lyndon trees. The second part studies rst the limit distribution of an additive functional on Cayley trees, then a new type of a one dimensional percolation model that can be seen as the study of cars parking after a random walk.
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Submitted on : Thursday, March 29, 2018 - 10:39:32 AM
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  • HAL Id : tel-01746520, version 1



Elahe Zohoorianazad. Comportement asymptotique des mots aléatoires et des arbres aléatoires, et applications. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2007. Français. ⟨NNT : 2007NAN10034⟩. ⟨tel-01746520⟩



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