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

@article{Jung2017DelocalizationAL, 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}, year={2017}, volume={23} }

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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