How fast can the chord-length distribution decay?

Abstract : The modelling of random bi-phasic, or porous, media has been, and still is, under active investigation by mathematicians, physicists or physicians. In this paper we consider a thresholded random process $X$ as a source of the two phases. The intervals when $X$ is in a given phase, named chords, are the subject of interest. We focus on the study of the tails of the chord-length distribution functions. In the literature, different types of the tail behavior have been reported, among them exponential-like or power-like decay. We look for the link between the dependence structure of the underlying thresholded process $X$ and the rate of decay of the chord-length distribution. When the process $X$ is a stationary Gaussian process, we relate the latter to the rate at which the covariance function of $X$ decays at large lags. We show that exponential, or nearly exponential, decay of the tail of the distribution of the chord-lengths is very common, perhaps surprisingly so.
Type de document :
Article dans une revue
Advances in Applied Probability, Applied Probability Trust, 2011, 43 (2), pp.504-523
Liste complète des métadonnées

Littérature citée [16 références]  Voir  Masquer  Télécharger
Contributeur : Anne Estrade <>
Soumis le : vendredi 22 juillet 2011 - 17:18:25
Dernière modification le : jeudi 11 janvier 2018 - 06:12:27
Document(s) archivé(s) le : vendredi 4 novembre 2011 - 15:15:16


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-00419202, version 2



Yann Demichel, Anne Estrade, Marie Kratz, Gennady Samorodnitsky. How fast can the chord-length distribution decay?. Advances in Applied Probability, Applied Probability Trust, 2011, 43 (2), pp.504-523. 〈hal-00419202v2〉



Consultations de la notice


Téléchargements de fichiers