How fast can the chord-length distribution decay ?

Yann Demichel (MAP5, Université Paris 5)
vendredi 12 février 2010

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
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.

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).