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When are increment-stationary random point sets stationary?


 
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1. Title Title of document When are increment-stationary random point sets stationary?
 
2. Creator Author's name, affiliation, country Antoine Gloria; Université Libre de Bruxelles & Inria Lille-Nord Europe; Belgium
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random geometry; random point sets; thermodynamic limit; stochastic homogenization
 
3. Subject Subject classification 60D05; 39A70;60H25
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR-10-JCJC-0106 AMAM
 
7. Date (YYYY-MM-DD) 2014-05-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3288
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3288
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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