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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/248337

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spelling 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
dc.relation.none.fl_str_mv 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
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
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