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On the eigenvalues and eigenvectors of an overlapping Markov chain
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  • Published: 02 January 2004

On the eigenvalues and eigenvectors of an overlapping Markov chain

  • Abbas Alhakim1 

Probability Theory and Related Fields volume 128, pages 589–605 (2004)Cite this article

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Abstract.

Starting with a sequence of i.i.d. [uniform] random variables with m possible values, we consider the overlapping Markov chain formed by sliding a window of size k through the i.i.d. sequence. We study the limiting covariance matrix B k of this Markov chain and give algorithms for constructing the eigenvectors of B k . We also discuss the applicability of the results in strengthening Pearson’s χ2 test as well as the relation to approximate entropy and the usefulness in the area of testing the hypothesis of uniformity of random number generators.

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References

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Authors and Affiliations

  1. Division of Mathematics and Computer Science, Clarkson University, Potsdam, NY, 13676, USA

    Abbas Alhakim

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  1. Abbas Alhakim
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Correspondence to Abbas Alhakim.

Additional information

Mathematics Subject Classification (2000): Primary: 60J10; Secondary: 11K45

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Cite this article

Alhakim, A. On the eigenvalues and eigenvectors of an overlapping Markov chain. Probab. Theory Relat. Fields 128, 589–605 (2004). https://doi.org/10.1007/s00440-003-0321-z

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  • Received: 28 July 2002

  • Revised: 03 November 2003

  • Published: 02 January 2004

  • Issue Date: April 2004

  • DOI: https://doi.org/10.1007/s00440-003-0321-z

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Keywords

  •  Finite Markov Chains
  • Testing of Random Number Generators
  • Limiting covariance matrix
  • Chi-square statistic
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