Delocalization and limiting spectral distribution of Erdős-Rényi graphs with constant expected degree

  title={Delocalization and limiting spectral distribution of Erdős-R{\'e}nyi graphs with constant expected degree},
  author={Paul Jung and Jaehun Lee},
  journal={Electronic Communications in Probability},
  • Paul Jung, Jaehun Lee
  • Published 19 October 2017
  • Mathematics
  • Electronic Communications in Probability
We consider Erd\H{o}s-R\'{e}nyi graphs $G(n,p_n)$ with large constant expected degree $\lambda$ and $p_n=\lambda/n$. Bordenave and Lelarge (2010) showed that the infinite-volume limit, in the Benjamini-Schramm topology, is a Galton-Watson tree with offspring distribution Pois($\lambda$) and the mean spectrum at the root of this tree has unbounded support and corresponds to the limiting spectral distribution of $G(n,p_n)$ as $n\to\infty$. We show that if one weights the edges by $1/\sqrt{\lambda… Expand
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