Universal bounds on the selfaveraging of random diffraction measures.
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| Název: | Universal bounds on the selfaveraging of random diffraction measures. |
|---|---|
| Autoři: | Külske, Christof |
| Zdroj: | Probability Theory & Related Fields; 2003, Vol. 126 Issue 1, p29, 22p |
| Témata: | DIFFRACTION patterns, RANDOM measures, MATHEMATICAL functions |
| Abstrakt: | We consider diffraction at random point scatterers on general discrete point sets in ℝ[sup ν] , restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers. The rate is given in terms of a universal function that depends on the point set only through the minimal distance between points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a central limit theorem. [ABSTRACT FROM AUTHOR] |
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| Databáze: | Complementary Index |
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| Header | DbId: edb DbLabel: Complementary Index An: 9705863 RelevancyScore: 832 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 831.771301269531 |
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| Items | – Name: Title Label: Title Group: Ti Data: Universal bounds on the selfaveraging of random diffraction measures. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Külske%2C+Christof%22">Külske, Christof</searchLink> – Name: TitleSource Label: Source Group: Src Data: Probability Theory & Related Fields; 2003, Vol. 126 Issue 1, p29, 22p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22DIFFRACTION+patterns%22">DIFFRACTION patterns</searchLink><br /><searchLink fieldCode="DE" term="%22RANDOM+measures%22">RANDOM measures</searchLink><br /><searchLink fieldCode="DE" term="%22MATHEMATICAL+functions%22">MATHEMATICAL functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider diffraction at random point scatterers on general discrete point sets in ℝ[sup ν] , restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers. The rate is given in terms of a universal function that depends on the point set only through the minimal distance between points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a central limit theorem. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Probability Theory & Related Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 29 Subjects: – SubjectFull: DIFFRACTION patterns Type: general – SubjectFull: RANDOM measures Type: general – SubjectFull: MATHEMATICAL functions Type: general Titles: – TitleFull: Universal bounds on the selfaveraging of random diffraction measures. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Külske, Christof IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 2003 Type: published Y: 2003 Identifiers: – Type: issn-print Value: 01788051 Numbering: – Type: volume Value: 126 – Type: issue Value: 1 Titles: – TitleFull: Probability Theory & Related Fields Type: main |
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