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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 2, Pages 399–402
DOI: https://doi.org/10.4213/tvp293 (Mi tvp293) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

Distribution of the fractional parts of random vectors: The Gaussian case. I

A. A. Kulikovaa, Yu. V. Prokhorovb

a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (346 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp293
Abstract: The paper considers a fractional distribution of an $s$-dimensional Gaussian random vector. Inequalities for the distribution deviation from the uniform distribution are proved. The proofs use the Poisson summation formula and some facts from the theory of representation of integers by square forms. The main attention of this part of the paper is devoted to the case of small values of $s$. The case of large values of $s$ will be consider additionally.
Keywords: uniform distribution, Poisson summation formula, fractional Gaussian vectors.
Received: 15.04.2003
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 2, Pages 355–359
DOI: https://doi.org/10.1137/S0040585X9780452
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Kulikova, Yu. V. Prokhorov, “Distribution of the fractional parts of random vectors: The Gaussian case. I”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 399–402; Theory Probab. Appl., 48:2 (2004), 355–359
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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  • https://doi.org/10.4213/tvp293
  • https://www.mathnet.ru/eng/tvp/v48/i2/p399
    Cycle of papers
    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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