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- W4313561043 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 $Theta(n^2)$ with $n$ the size of the state space. The proof approach is split into two parts. First, we introduce a class of symmetric random matrices with dependent entries called approximately uncorrelated random matrices with variance profile. We establish their limiting eigenvalue distributions by means of the moment method. Second, we develop a coupling argument to show that this general-purpose result applies to the singular value distributions associated with the block Markov chain." @default.
- W4313561043 created "2023-01-06" @default.
- W4313561043 creator A5004989436 @default.
- W4313561043 creator A5090443963 @default.
- W4313561043 date "2023-04-01" @default.
- W4313561043 modified "2023-09-25" @default.
- W4313561043 title "Singular value distribution of dense random matrices with block Markovian dependence" @default.
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- W4313561043 doi "https://doi.org/10.1016/j.spa.2023.01.001" @default.
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