A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée
- Autores
- Cesaratto, Eda
- Año de publicación
- 2009
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The paper “Euclidean algorithms are Gaussian” [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386], is devoted to the distributional analysis of three variants of Euclidean algorithms. The Central Limit Theorem and the Local Limit Theorem obtained there are the first ones in the context of the “dynamical analysis” method. The techniques developed have been applied in further various works (e.g. [V. Baladi, A. Hachemi, A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs, Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 749–770; E. Cesaratto, J. Clément, B. Daireaux, L. Lhote, V. Maume, B. Vallée, Analysis of fast versions of the Euclid algorithm, in: Proceedings of Third Workshop on Analytic Algorithmics and Combinatorics, ANALCO'08, SIAM, 2008; E. Cesaratto, A. Plagne, B. Vallée, On the non-randomness of modular arithmetic progressions, in: Fourth Colloquium on Mathematics and Computer Science. Algorithms, Trees, Combinatorics and Probabilities, in: Discrete Math. Theor. Comput. Sci. Proc., vol. AG, 2006, pp. 271–288]). These theorems are proved first for an auxiliary probabilistic model, called “the smoothed model,” and after, the estimates are transferred to the “true” probabilistic model. In this note, we remark that “the smoothed model” described in [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386] is not adapted to this transfer and replaces it by an adapted one. However, the results remain unchanged.
Fil: Cesaratto, Eda. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina - Materia
-
Distributional analysis
Euclidean algorithms - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/248337
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A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. ValléeCesaratto, EdaDistributional analysisEuclidean algorithmshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The paper “Euclidean algorithms are Gaussian” [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386], is devoted to the distributional analysis of three variants of Euclidean algorithms. The Central Limit Theorem and the Local Limit Theorem obtained there are the first ones in the context of the “dynamical analysis” method. The techniques developed have been applied in further various works (e.g. [V. Baladi, A. Hachemi, A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs, Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 749–770; E. Cesaratto, J. Clément, B. Daireaux, L. Lhote, V. Maume, B. Vallée, Analysis of fast versions of the Euclid algorithm, in: Proceedings of Third Workshop on Analytic Algorithmics and Combinatorics, ANALCO'08, SIAM, 2008; E. Cesaratto, A. Plagne, B. Vallée, On the non-randomness of modular arithmetic progressions, in: Fourth Colloquium on Mathematics and Computer Science. Algorithms, Trees, Combinatorics and Probabilities, in: Discrete Math. Theor. Comput. Sci. Proc., vol. AG, 2006, pp. 271–288]). These theorems are proved first for an auxiliary probabilistic model, called “the smoothed model,” and after, the estimates are transferred to the “true” probabilistic model. In this note, we remark that “the smoothed model” described in [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386] is not adapted to this transfer and replaces it by an adapted one. However, the results remain unchanged.Fil: Cesaratto, Eda. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaAcademic Press Inc Elsevier Science2009-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/248337Cesaratto, Eda; A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée; Academic Press Inc Elsevier Science; Journal Of Number Theory; 129; 10; 10-2009; 2267-22730022-314XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022314X09001139info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jnt.2009.02.018info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:09:53Zoai:ri.conicet.gov.ar:11336/248337instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:09:53.68CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée |
title |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée |
spellingShingle |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée Cesaratto, Eda Distributional analysis Euclidean algorithms |
title_short |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée |
title_full |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée |
title_fullStr |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée |
title_full_unstemmed |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée |
title_sort |
A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée |
dc.creator.none.fl_str_mv |
Cesaratto, Eda |
author |
Cesaratto, Eda |
author_facet |
Cesaratto, Eda |
author_role |
author |
dc.subject.none.fl_str_mv |
Distributional analysis Euclidean algorithms |
topic |
Distributional analysis Euclidean algorithms |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
The paper “Euclidean algorithms are Gaussian” [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386], is devoted to the distributional analysis of three variants of Euclidean algorithms. The Central Limit Theorem and the Local Limit Theorem obtained there are the first ones in the context of the “dynamical analysis” method. The techniques developed have been applied in further various works (e.g. [V. Baladi, A. Hachemi, A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs, Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 749–770; E. Cesaratto, J. Clément, B. Daireaux, L. Lhote, V. Maume, B. Vallée, Analysis of fast versions of the Euclid algorithm, in: Proceedings of Third Workshop on Analytic Algorithmics and Combinatorics, ANALCO'08, SIAM, 2008; E. Cesaratto, A. Plagne, B. Vallée, On the non-randomness of modular arithmetic progressions, in: Fourth Colloquium on Mathematics and Computer Science. Algorithms, Trees, Combinatorics and Probabilities, in: Discrete Math. Theor. Comput. Sci. Proc., vol. AG, 2006, pp. 271–288]). These theorems are proved first for an auxiliary probabilistic model, called “the smoothed model,” and after, the estimates are transferred to the “true” probabilistic model. In this note, we remark that “the smoothed model” described in [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386] is not adapted to this transfer and replaces it by an adapted one. However, the results remain unchanged. Fil: Cesaratto, Eda. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina |
description |
The paper “Euclidean algorithms are Gaussian” [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386], is devoted to the distributional analysis of three variants of Euclidean algorithms. The Central Limit Theorem and the Local Limit Theorem obtained there are the first ones in the context of the “dynamical analysis” method. The techniques developed have been applied in further various works (e.g. [V. Baladi, A. Hachemi, A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs, Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 749–770; E. Cesaratto, J. Clément, B. Daireaux, L. Lhote, V. Maume, B. Vallée, Analysis of fast versions of the Euclid algorithm, in: Proceedings of Third Workshop on Analytic Algorithmics and Combinatorics, ANALCO'08, SIAM, 2008; E. Cesaratto, A. Plagne, B. Vallée, On the non-randomness of modular arithmetic progressions, in: Fourth Colloquium on Mathematics and Computer Science. Algorithms, Trees, Combinatorics and Probabilities, in: Discrete Math. Theor. Comput. Sci. Proc., vol. AG, 2006, pp. 271–288]). These theorems are proved first for an auxiliary probabilistic model, called “the smoothed model,” and after, the estimates are transferred to the “true” probabilistic model. In this note, we remark that “the smoothed model” described in [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331–386] is not adapted to this transfer and replaces it by an adapted one. However, the results remain unchanged. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-10 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/248337 Cesaratto, Eda; A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée; Academic Press Inc Elsevier Science; Journal Of Number Theory; 129; 10; 10-2009; 2267-2273 0022-314X CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/248337 |
identifier_str_mv |
Cesaratto, Eda; A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée; Academic Press Inc Elsevier Science; Journal Of Number Theory; 129; 10; 10-2009; 2267-2273 0022-314X CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
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info:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022314X09001139 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jnt.2009.02.018 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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application/pdf application/pdf application/pdf |
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Academic Press Inc Elsevier Science |
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Academic Press Inc Elsevier Science |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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