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arXiv · 2405.08347

Tree walks and the spectrum of random graphs

Eva-Maria Hainzl·Élie de Panafieu
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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.

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Eva-Maria Hainzl, Élie de Panafieu. 2024-05-14. Tree walks and the spectrum of random graphs. https://arxiv.org/abs/2405.08347

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