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).