Random walk speed is a proper function on Teichmüller space
Resumen:
Consider a closed surface M with negative Euler characteristic, and an admissible probability measure on the fundamental group of M with a finite first moment. Corresponding to each point in the Teichmüller space of M , there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function on the Teichmüller space of M , and we relate the growth of the speed to the Teichmüller distance to a basepoint. One key argument is an adaptation of Gouëzel’s pivoting techniques to actions of a fixed group on a sequence of hyperbolic metric spaces.
| 2022 | |
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PIVOTING ARGUMENT SINGULARITY CONJETURE MATHEMATICS - GEOMETRIC TOPOLOGY MATHEMATICS -GROUPS THEORY MATHEMATICS - TOPOLOGY |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44638 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522809920880640 |
|---|---|
| author | Azemar, Aitor |
| author2 | Vaibhav, Gadre Gouëzel, Sébastien Haettel, Thomas Lessa Echeverriarza, Pablo Uyanik, Caglar |
| author2_role | author author author author author |
| author_facet | Azemar, Aitor Vaibhav, Gadre Gouëzel, Sébastien Haettel, Thomas Lessa Echeverriarza, Pablo Uyanik, Caglar |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Azemar Aitor Vaibhav Gadre Gouëzel Sébastien Haettel Thomas Lessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Uyanik Caglar |
| dc.creator.none.fl_str_mv | Azemar, Aitor Vaibhav, Gadre Gouëzel, Sébastien Haettel, Thomas Lessa Echeverriarza, Pablo Uyanik, Caglar |
| dc.date.accessioned.none.fl_str_mv | 2024-07-04T13:53:56Z |
| dc.date.available.none.fl_str_mv | 2024-07-04T13:53:56Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | Consider a closed surface M with negative Euler characteristic, and an admissible probability measure on the fundamental group of M with a finite first moment. Corresponding to each point in the Teichmüller space of M , there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function on the Teichmüller space of M , and we relate the growth of the speed to the Teichmüller distance to a basepoint. One key argument is an adaptation of Gouëzel’s pivoting techniques to actions of a fixed group on a sequence of hyperbolic metric spaces. |
| dc.description.es.fl_txt_mv | Versión permitida preprint. Publicado también en: Journal of Modern Dynamics, 2023, 19 : 815–832. DOI: 10.3934/jmd.2023022 |
| dc.format.extent.es.fl_str_mv | 18 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Aitor, A, Vaibhav, G, Gouëzel, S, Haettel, T, Y y otros. "Random walk speed is a proper function on Teichmüller space". [Preprint]. Publicado en: Mathematics (Geometric Topology). 2022, arXiv:2212.06581, dic. 2022 pp 1-14..3934/jmd.2023022 |
| dc.identifier.doi.none.fl_str_mv | arXiv:2212.06581 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/44638 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Geometric Topology), arXiv:2212.06581, dic. 2022, pp.1-14 |
| 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.other.es.fl_str_mv | PIVOTING ARGUMENT SINGULARITY CONJETURE MATHEMATICS - GEOMETRIC TOPOLOGY MATHEMATICS -GROUPS THEORY MATHEMATICS - TOPOLOGY |
| dc.title.none.fl_str_mv | Random walk speed is a proper function on Teichmüller space |
| 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 | Versión permitida preprint. Publicado también en: Journal of Modern Dynamics, 2023, 19 : 815–832. DOI: 10.3934/jmd.2023022 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_8ea74cf4b4819db17e2492635143e7a4 |
| identifier_str_mv | Aitor, A, Vaibhav, G, Gouëzel, S, Haettel, T, Y y otros. "Random walk speed is a proper function on Teichmüller space". [Preprint]. Publicado en: Mathematics (Geometric Topology). 2022, arXiv:2212.06581, dic. 2022 pp 1-14..3934/jmd.2023022 arXiv:2212.06581 |
| 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:20.500.12008/44638 |
| publishDate | 2022 |
| 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 | Azemar AitorVaibhav GadreGouëzel SébastienHaettel ThomasLessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Uyanik Caglar2024-07-04T13:53:56Z2024-07-04T13:53:56Z2022Aitor, A, Vaibhav, G, Gouëzel, S, Haettel, T, Y y otros. "Random walk speed is a proper function on Teichmüller space". [Preprint]. Publicado en: Mathematics (Geometric Topology). 2022, arXiv:2212.06581, dic. 2022 pp 1-14..3934/jmd.2023022https://hdl.handle.net/20.500.12008/44638arXiv:2212.06581Versión permitida preprint. Publicado también en: Journal of Modern Dynamics, 2023, 19 : 815–832. DOI: 10.3934/jmd.2023022Consider a closed surface M with negative Euler characteristic, and an admissible probability measure on the fundamental group of M with a finite first moment. Corresponding to each point in the Teichmüller space of M , there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function on the Teichmüller space of M , and we relate the growth of the speed to the Teichmüller distance to a basepoint. One key argument is an adaptation of Gouëzel’s pivoting techniques to actions of a fixed group on a sequence of hyperbolic metric spaces.Submitted by Egaña Florencia (florega@gmail.com) on 2024-06-26T15:33:41Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 10.3934_jmd.2023022-1.pdf: 237182 bytes, checksum: 2460d03f1a2dc31170dca28e8a061a3e (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-06-27T17:03:58Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 10.3934_jmd.2023022-1.pdf: 237182 bytes, checksum: 2460d03f1a2dc31170dca28e8a061a3e (MD5)Rejected by Luna Fabiana (fabiana.luna@seciu.edu.uy), reason: Hola Florencia, Estuvimos mirando con Mabel la Licencia de este artículo en Sherpa Romeo y vimos que se permite subirlo con el path B cuya licencia es CC-BY, por lo tanto te vamos a pedir que lo subas de nuevo, tenés que subir todo el registro de nuevo, porque el sistema le asigna archivos internos una vez que se elige el tipo de licencia, y no basta con cambiar el nombre de la licencia, hay que borrar el registro y subirlo de nuevo. Muchas Gracias . Fabiana on 2024-06-28T16:55:43Z (GMT)Submitted by Egaña Florencia (florega@gmail.com) on 2024-07-03T21:36:25Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2212.06581v1.pdf: 264146 bytes, checksum: 9a0d1939577a592fdf88d66cae1f877e (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-07-04T10:51:22Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2212.06581v1.pdf: 264146 bytes, checksum: 9a0d1939577a592fdf88d66cae1f877e (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-07-04T13:53:56Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2212.06581v1.pdf: 264146 bytes, checksum: 9a0d1939577a592fdf88d66cae1f877e (MD5) Previous issue date: 202218 p.application/pdfenengarXivMathematics (Geometric Topology), arXiv:2212.06581, dic. 2022, pp.1-14Las 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)PIVOTING ARGUMENTSINGULARITY CONJETUREMATHEMATICS - GEOMETRIC TOPOLOGYMATHEMATICS -GROUPS THEORYMATHEMATICS - TOPOLOGYRandom walk speed is a proper function on Teichmüller spacePreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAzemar, AitorVaibhav, GadreGouëzel, SébastienHaettel, ThomasLessa Echeverriarza, PabloUyanik, CaglarLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44638/10/license.txt6429389a7df7277b72b7924fdc7d47a9MD510CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/44638/7/license_urla006180e3f5b2ad0b88185d14284c0e0MD57license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Random walk speed is a proper function on Teichmüller space Azemar, Aitor PIVOTING ARGUMENT SINGULARITY CONJETURE MATHEMATICS - GEOMETRIC TOPOLOGY MATHEMATICS -GROUPS THEORY MATHEMATICS - TOPOLOGY |
| status_str | submittedVersion |
| title | Random walk speed is a proper function on Teichmüller space |
| title_full | Random walk speed is a proper function on Teichmüller space |
| title_fullStr | Random walk speed is a proper function on Teichmüller space |
| title_full_unstemmed | Random walk speed is a proper function on Teichmüller space |
| title_short | Random walk speed is a proper function on Teichmüller space |
| title_sort | Random walk speed is a proper function on Teichmüller space |
| topic | PIVOTING ARGUMENT SINGULARITY CONJETURE MATHEMATICS - GEOMETRIC TOPOLOGY MATHEMATICS -GROUPS THEORY MATHEMATICS - TOPOLOGY |
| url | https://hdl.handle.net/20.500.12008/44638 |
