108 research outputs found
In search of relativistic time
This paper explores the status of some notions which are usually associated
to time, like datations, chronology, durations, causality, cosmic time and time
functions in the Einsteinian relativistic theories. It shows how, even if some
of these notions do exist in the theory or for some particular solution of it,
they appear usually in mutual conflict: they cannot be synthesized coherently,
and this is interpreted as the impossibility to construct a common entity which
could be called time. This contrasts with the case in Newtonian physics where
such a synthesis precisely constitutes Newtonian time. After an illustration by
comparing the status of time in Einsteinian physics with that of the vertical
direction in Newtonian physics, I will conclude that there is no pertinent
notion of time in Einsteinian theories.Comment: to appear in Studies in History and Philosophy of Science Part B:
Studies in History and Philosophy of Modern Physic
Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U-statistics
Continuing the analysis initiated in Lachi\'eze-Rey and Peccati (2011), we
use contraction operators to study the normal approximation of random variables
having the form of a U-statistic written on the points in the support of a
random Poisson measure. Applications are provided: to boolean models, and
coverage of random networks
Random Measurable Sets and Covariogram Realisability Problems
We provide a characterization of the realisable set covariograms, bringing a
rigorous yet abstract solution to the problem in materials science. Our
method is based on the covariogram functional for random mesurable sets (RAMS)
and on a result about the representation of positive operators in a locally
compact space. RAMS are an alternative to the classical random closed sets in
stochastic geometry and geostatistics, they provide a weaker framework allowing
to manipulate more irregular functionals, such as the perimeter. We therefore
use the illustration provided by the problem to advocate the use of
RAMS for solving theoretical problems of geometric nature. Along the way, we
extend the theory of random measurable sets, and in particular the local
approximation of the perimeter by local covariograms.Comment: 35p
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