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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 2, Pages 399–402 (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

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.

DOI: https://doi.org/10.4213/tvp293

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English version:
Theory of Probability and its Applications, 2004, 48:2, 355–359

Bibliographic databases:

Received: 15.04.2003

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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    This publication is cited in the following articles:
    1. V. I. Khokhlov, “The uniform distribytion on sphere in $R^s$. I. Properties of projections”, Theory Probab. Appl., 50:3 (2006), 386–399  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. Ya. Kuznetsova, “On the convergence to uniform distribution”, Theory Probab. Appl., 50:4 (2006), 687–689  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. A. Kulikova, Yu. V. Prokhorov, V. I. Khokhlov, “Distribution of fractional parts of random vectors: Gaussian case. II”, Theory Probab. Appl., 50:4 (2006), 685–687  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. O. V. Viskov, V. I. Khokhlov, “Four areas of Yu. V. Prokhorov's studies and their perspectives”, Theory Probab. Appl., 60:2 (2016), 336–342  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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