Singular value distribution of Nhat.
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Singular value distribution of dense random matrices with block Markovian dependence

We have submitted Singular value distribution of dense random matrices with block Markovian dependence, and it is currently under review. This is joint work between Alexander Van Werde and myself. A preprint is available on arXiv.


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.
The proof approach is split into two parts. First, we introduce a class of symmetric random matrices with dependence 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 block Markov chains.


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Jaron Sanders received in 2012 M.Sc. degrees in Mathematics and Physics from the Eindhoven University of Technology, The Netherlands, as well as a PhD degree in Mathematics in 2016. After he obtained his PhD degree, he worked as a post-doctoral researcher at the KTH Royal Institute of Technology in Stockholm, Sweden. Jaron Sanders then worked as an assistant professor at the Delft University of Technology, and now works as an assistant professor at the Eindhoven University of Technology. His research interests are applied probability, queueing theory, stochastic optimization, stochastic networks, wireless networks, and interacting (particle) systems.