Random Measurable Sets and Covariogram Realisability Problems

Abstract : We provide a characterization of the realisable set covariograms, bringing a rigorous yet abstract solution to the $S_2$ 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 $S_{2}$ 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.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00995853
Contributor : Raphael Lachieze-Rey <>
Submitted on : Saturday, February 28, 2015 - 2:09:05 AM
Last modification on : Thursday, April 11, 2019 - 4:02:09 PM
Document(s) archivé(s) le : Friday, May 29, 2015 - 10:06:57 AM

Files

reaper_final.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00995853, version 3
  • ARXIV : 1405.6333

Collections

Citation

Bruno Galerne, Raphaël Lachièze-Rey. Random Measurable Sets and Covariogram Realisability Problems. Advances in Applied Probability, Applied Probability Trust, 2015, 47 (3), pp.611-639. 〈http://projecteuclid.org/current/euclid.aap〉. 〈hal-00995853v3〉

Share

Metrics

Record views

226

Files downloads

98