Nicolas Pouyanne

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Pólya processes are natural generalization of Pólya-Eggenberger urn models. This article presents a new approach of their asymptotic behaviour via moments, based on the spectral decomposition of a suitable finite difference transition operator on polynomial functions. Especially, it provides new results for large processes (a Pólya process is called small(More)
This article deals with Pólya generalized urn models with constant balance in any dimension. It is based on the algebraic approach of Pouyanne (2005) and classifies urns having “large” eigenvalues in five classes, depending on their almost sure asymptotics. These classes are described in terms of the spectrum of the urn’s replacement matrix and examples of(More)
A “hybrid method”, dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux’s method and singularity analysis theory. This hybrid method applies to functions that remain of moderate growth near the unit circle and satisfy suitable smoothness assumptions—this, even in the case when the unit(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)