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Singular value distribution of dense random matrices with block Markovian dependence

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  • Sanders, Jaron
  • Van Werde, Alexander

Abstract

A block Markov chain is a Markov chain whose state space can be partitioned into a finite number of clusters such that the transition probabilities only depend on the clusters. Block Markov chains thus serve as a model for Markov chains with communities. This paper establishes limiting laws for the singular value distributions of the empirical transition matrix and empirical frequency matrix associated to a sample path of the block Markov chain whenever the length of the sample path is Θ(n2) with n the size of the state space.

Suggested Citation

  • Sanders, Jaron & Van Werde, Alexander, 2023. "Singular value distribution of dense random matrices with block Markovian dependence," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 453-504.
    • Handle: RePEc:eee:spapps:v:158:y:2023:i:c:p:453-504
    DOI: 10.1016/j.spa.2023.01.001
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    References listed on IDEAS

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