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- Brigitte Chauvin, Philippe Flajolet, Danièle Gardy, Bernhard Gittenberger
- Combinatorics, Probability & Computing
- 2004

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)

We consider a two colors Pólya urn with balance S. Assume it is a large urn i.e. the second eigenvalue m of the replacement matrix satisfies 1/2 < m/S ≤ 1. After n drawings, the composition vector has asymptotically a first deterministic term of order n and a second random term of order n m/S. The object of interest is the limit distribution of this random… (More)

A classical random walk (S t , t ∈ N) is defined by S t := t n=0 X n , where (X n) are i.i.d. When the increments (X n) n∈N are a one-order Markov chain, a short memory is introduced in the dynamics of (S t). This so-called " persistent " random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated… (More)

- Brigitte Chauvin, Nicolas Pouyanne
- Random Struct. Algorithms
- 2004

- Brigitte Chauvin, Michael Drmota
- Algorithmica
- 2006

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 define a probability distribution over the set of Boolean functions of k variables induced by the tree representation of Boolean expressions. The law we are interested in is inspired by the growth model of Binary Search Trees: we call it the growing tree law. We study it over different logical systems and compare the results we obtain to already known… (More)

- Brigitte Chauvin, Danièle Gardy, Cécile Mailler
- Random Struct. Algorithms
- 2015

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)

Consider a balanced non triangular two-color Pólya-Eggenberger urn process, assumed to be large which means that the ratio σ of the replacement matrix eigenvalues satisfies 1/2 < σ < 1. The composition vector of both discrete time and continuous time models admits a drift which is carried by the principal direction of the replacement matrix. In the second… (More)

- Peggy Cénac, Brigitte Chauvin, Frédéric Paccaut, Nicolas Pouyanne
- Random Struct. Algorithms
- 2015

Common assumptions on the source producing the words inserted in a suffix trie with n leaves lead to a ln n 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 ln n. Both are built from VLMC (Variable Length Markov Chain)… (More)