How fast can the chord-length distribution decay ?
Résumé : The modelling of random bi-phasic, or porous, media has been, and still is, under active investigation by mathematicians, physicists or physicians. In this talk we consider a thresholded random process as a source of the two phases. The intervals when 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 and the rate of decay of the chord-length distribution. When the process is a stationary Gaussian process, we relate the latter to the rate at which the covariance function of 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.
Cet exposé se tiendra en salle C20-13, 20ème étage, Université Paris 1, Centre Pierre Mendes-France, 90 rue de Tolbiac, 75013 Paris (métro : Olympiades).