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Tree Walks and the Spectrum of Random Graphs

Authors Eva-Maria Hainzl , Élie de Panafieu

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ACM Subject Classification
  • Mathematics of computing → Generating functions
  • Mathematics of computing → Spectra of graphs
Keywords
  • Spectrum of random matrices
  • generating functions

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Abstract

It is a classic result in spectral theory that the limit distribution of the spectral measure of random graphs G(n,p) converges to the semicircle law in case np tends to infinity with n. The spectral measure for random graphs G(n,c/n) however is less understood. In this work, we combine and extend two combinatorial approaches by Bauer and Golinelli (2001) and Enriquez and Menard (2016) and approximate the moments of the spectral measure by counting walks that span trees.

Cite As Get BibTex

Eva-Maria Hainzl and Élie de Panafieu. Tree Walks and the Spectrum of Random Graphs. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.AofA.2024.11

Author Details

Eva-Maria Hainzl
  • TU Wien, Austria
Élie de Panafieu
  • Nokia Bell Labs, Nozay, France

Funding

This work was supported by the RandNET project, MSCA-RISE - Marie Skłodowska-Curie Research and Innovation Staff Exchange Programme (RISE), Grant agreement 101007705.
  • Hainzl, Eva-Maria: This work was partially founded by the Austrian Science Foundation FWF, projects F50-02, F55-02.

Acknowledgements

We thank Nicolas Curien and Laurent Ménard for encouraging us to work on this topic, their availability and their insights on the spectrum of random graphs. We also thank the Institut de Recherche en Informatique Fondamentale (IRIF), Université Paris Cité, for hosting us.

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