Title :

When are increment-stationary random point sets stationary?

Author(s) :

Gloria, Antoine [Auteur]
Département de Mathématique [Bruxelles] [ULB]
Quantitative methods for stochastic models in physics [MEPHYSTO]

Journal title :

Electronic Communications in Probability

Pages :

1-14

Publisher :

Institute of Mathematical Statistics (IMS)

Publication date :

2014-05-18

ISSN :

1083-589X

English keyword(s) :

random geometry
random point sets
thermodynamic limit
stochastic homogenization.
stochastic homogenization

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In a recent work, Blanc, Le Bris, and Lions defined a notion of increment-stationarity for random point sets, which allowed them to prove the existence of a thermodynamic limit for two-body potential energies on such point ...
Show more >In a recent work, Blanc, Le Bris, and Lions defined a notion of increment-stationarity for random point sets, which allowed them to prove the existence of a thermodynamic limit for two-body potential energies on such point sets (under the additional assumption of ergodicity), and to introduce a variant of stochastic homogenization for increment-stationary coefficients. Whereas stationary random point sets are increment-stationary, it is not clear a priori under which conditions increment-stationary random point sets are stationary. In the present contribution, we give a characterization of the equivalence of both notions of stationarity based on elementary PDE theory in the probability space. This allows us to give conditions on the decay of a covariance function associated with the random point set, which ensure that increment-stationary random point sets are stationary random point sets up to a random translation with bounded second moment in dimensions $d>2$. In dimensions $d=1$ and $d=2$, we show that such sufficient conditions cannot exist.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL