#### Filter Results:

- Full text PDF available (17)

#### Publication Year

2001

2015

- This year (0)
- Last 5 years (7)
- Last 10 years (13)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

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)

- 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)

- 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)

Abstract. 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. The object of interest is the limit distribution of this… (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)

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)

- 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 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)