Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems
Resumen:
We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This paper is a continuation of {\it Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems} by the same authors in which the square case was considered. Our main tools are the Kac-Rice formula for the second moment of the volume of the zero set and an expansion of this random variable into the Itô-Wiener Chaos.
| 2021 | |
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Kostlan–Shub–Smale random polynomial systems Co-area formula Kac-Rice formula Central limit theorem |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38119 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522796308267008 |
|---|---|
| author | Azaïs, J.M. |
| author2 | Armentano, Diego Dalmao Artigas, Federico León, José Rafael |
| author2_role | author author author |
| author_facet | Azaïs, J.M. Armentano, Diego Dalmao Artigas, Federico León, José Rafael |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Azaïs J.M., Université de Toulouse Armentano Diego, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Dalmao Artigas Federico, Universidad de la República (Uruguay). CENUR. León José Rafael, Universidad de la República (Uruguay). Facultad de Ingeniería |
| dc.creator.none.fl_str_mv | Azaïs, J.M. Armentano, Diego Dalmao Artigas, Federico León, José Rafael |
| dc.date.accessioned.none.fl_str_mv | 2023-07-13T13:11:22Z |
| dc.date.available.none.fl_str_mv | 2023-07-13T13:11:22Z |
| dc.date.issued.none.fl_str_mv | 2021 |
| dc.description.abstract.none.fl_txt_mv | We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This paper is a continuation of {\it Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems} by the same authors in which the square case was considered. Our main tools are the Kac-Rice formula for the second moment of the volume of the zero set and an expansion of this random variable into the Itô-Wiener Chaos. |
| dc.description.es.fl_txt_mv | Publicado también como: American Journal of Mathematics, 2021, 143(4): 1011-1042. DOI: 10.1353/ajm.2021.0026 |
| dc.format.extent.es.fl_str_mv | 17 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Azaïs, J, Armentano, D, Dalmao Artigas, F [y otro autor] "Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems". [Preprint]. Publicado en: Mathematics (Probability). 2021 arXiv:1801.06331, Sep 2021, pp 1-17 . |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/38119 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Probability), arXiv:1801.06331, Sep 2021, pp 1-17 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Kostlan–Shub–Smale random polynomial systems Co-area formula Kac-Rice formula Central limit theorem |
| dc.title.none.fl_str_mv | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Publicado también como: American Journal of Mathematics, 2021, 143(4): 1011-1042. DOI: 10.1353/ajm.2021.0026 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_f7dc9f737f66993de5f33f763b94e877 |
| identifier_str_mv | Azaïs, J, Armentano, D, Dalmao Artigas, F [y otro autor] "Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems". [Preprint]. Publicado en: Mathematics (Probability). 2021 arXiv:1801.06331, Sep 2021, pp 1-17 . |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/38119 |
| publishDate | 2021 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Azaïs J.M., Université de ToulouseArmentano Diego, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Dalmao Artigas Federico, Universidad de la República (Uruguay). CENUR.León José Rafael, Universidad de la República (Uruguay). Facultad de Ingeniería2023-07-13T13:11:22Z2023-07-13T13:11:22Z2021Azaïs, J, Armentano, D, Dalmao Artigas, F [y otro autor] "Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems". [Preprint]. Publicado en: Mathematics (Probability). 2021 arXiv:1801.06331, Sep 2021, pp 1-17 .https://hdl.handle.net/20.500.12008/38119Publicado también como: American Journal of Mathematics, 2021, 143(4): 1011-1042. DOI: 10.1353/ajm.2021.0026We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This paper is a continuation of {\it Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems} by the same authors in which the square case was considered. Our main tools are the Kac-Rice formula for the second moment of the volume of the zero set and an expansion of this random variable into the Itô-Wiener Chaos.Submitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-07-13T11:18:03Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1808.02967.pdf: 295497 bytes, checksum: 4d644c8de1dc261f2789a3cba5154836 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-07-13T11:36:39Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1808.02967.pdf: 295497 bytes, checksum: 4d644c8de1dc261f2789a3cba5154836 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-07-13T13:11:22Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1808.02967.pdf: 295497 bytes, checksum: 4d644c8de1dc261f2789a3cba5154836 (MD5) Previous issue date: 202117 h.application/pdfenengarXivMathematics (Probability), arXiv:1801.06331, Sep 2021, pp 1-17Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Kostlan–Shub–Smale random polynomial systemsCo-area formulaKac-Rice formulaCentral limit theoremCentral Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systemsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAzaïs, J.M.Armentano, DiegoDalmao Artigas, FedericoLeón, José RafaelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/38119/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/38119/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems Azaïs, J.M. Kostlan–Shub–Smale random polynomial systems Co-area formula Kac-Rice formula Central limit theorem |
| status_str | submittedVersion |
| title | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems |
| title_full | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems |
| title_fullStr | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems |
| title_full_unstemmed | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems |
| title_short | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems |
| title_sort | Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems |
| topic | Kostlan–Shub–Smale random polynomial systems Co-area formula Kac-Rice formula Central limit theorem |
| url | https://hdl.handle.net/20.500.12008/38119 |
