Eda Cesaratto ; Alain Plagne ; Brigitte Vallée - On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold

dmtcs:3510 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3510
On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. ArnoldArticle

Authors: Eda Cesaratto 1; Alain Plagne 2; Brigitte Vallée ORCID3

We solve a problem by V. I. Arnold dealing with "how random" modular arithmetic progressions can be. After making precise how Arnold proposes to measure the randomness of a modular sequence, we show that this measure of randomness takes a simplified form in the case of arithmetic progressions. This simplified expression is then estimated using the methodology of dynamical analysis, which operates with tools coming from dynamical systems theory. In conclusion, this study shows that modular arithmetic progressions are far from behaving like purely random sequences, according to Arnold's definition.

https://doi.org/10.46298/dmtcs.3510
Source: HAL:hal-01184715v1
Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: transfer operators,dynamical analysis,Arnold's problems,bounds à la Dolgopyat,Perron Formula,Dirichlet series,modular arithmetic progressions,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

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