Brigitte Chauvin

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A classical random walk (St, t ∈ N) is defined by St := t ∑ n=0 Xn, where (Xn) are i.i.d. When the increments (Xn)n∈N are a one-order Markov chain, a short memory is introduced in the dynamics of (St). This so-called “persistent” random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated telegraph(More)
The purpose of this article is to show that the distribution of the longest fragment in the random multisection problem after k steps and the height of m-ary search trees (and some extensions) are not only closely related in a formal way but both can be asymptotically described with the same distribution function that has to be shifted in a proper way(More)
We consider boolean functions over n variables. Any such function can be represented (and computed) by a complete binary tree with and or or in the internal nodes and a literal in the external nodes, and many different trees can represent the same function, so that a fundamental question is related to the so-called complexity of a boolean function: L(f) :=(More)
Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical(More)
Common assumptions on the source producing the words inserted in a suffix trie with n leaves lead to a lnn height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of n and another one whose saturation level is negligible with respect to lnn. Both are built from VLMC (Variable Length Markov Chain)(More)
Abstract. In this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which one can visualize repetitions of subwords (seen as suffixes of subsequences). The CGRtree turns a sequence of letters into a Digital Search Tree (DST), obtained from the suffixes of the reversed sequence. Several results are known concerning the(More)
The space requirements of an m-ary search tree satisfy a well-known phase transition: when m ≤ 26, the second order asymptotics is Gaussian. When m ≥ 27, it is not Gaussian any longer and a limit W of a complex-valued martingale arises. We show that the distribution of W has a square integrable density on the complex plane, that its support is the whole(More)