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Local Law for Eigenvalues of Random Regular Bipartite Graphs

  • Linh V. TranEmail author
Article
  • 16 Downloads

Abstract

In this paper, we study the local law for eigenvalues of large random regular bipartite graphs with degree growing moderately fast. We prove that the empirical spectral distribution of the adjacency matrix converges in probability to a scaled down copy of the Marchenko–Pastur distribution on intervals of short length.

Keywords

Random bipartite regular graphs Marchenko–Pastur law Wishart matrix 

Mathematics Subject Classification

05C80 60G57 

Notes

Acknowledgements

The author thanks I. Dumitriu for bringing the problem to his attention. Part of this work was done while the author was at the Mathematics Department, University of Washington. The author also thanks the anonymous referee who provided many useful suggestions.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.International University - Vietnam National University HCMCHo Chi Minh CityVietnam

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