Convergence to the uniform distribution of vectors of partial sums modulo one with a common factor

DOI10.1007/s10959-024-01348-yMaRDI QIDQ6633184

Benjamin Jourdain, Unnamed Author

Publication date: 5 November 2024

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

zbMATH Keywords

Fourier transformcentral limit theoremBendford's lawsums modulo one

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Convergence of probability measures (60B10) General theory of distribution modulo (1) (11K06)

Cites Work

• Asymptotic development for the CLT in total variation distance
• A limit theorem for random sums modulo 1
• Limit theorems for distributions of sums reduced modulo a
• The distribution of leading digits and uniform distribution mod 1
• On error operators related to the arbitrary functions principle
• L'addition des variables aléatoires définies sur une circonférence.
• On the Asymptotic Uniform Distribution of Sums Reduced mod 1
• On Sums Modulo 2π of Independent Random Variables
• A Tool in Establishing Total Variation Convergence
• An Application of Fourier Series to the Most Significant Digit Problem
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