Title: Tree walks and the spectrum of random graphs Show Chinese title

Title: 树遍历和随机图的谱

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. Show Chinese abstract

Abstract: 这是谱理论中的经典结果，即当np随着n趋于无穷时，随机图G(n, p)的谱测度的极限分布收敛到半圆律。然而，对于随机图G(n, c/n)的谱测度则了解较少。在本工作中，我们结合并扩展了Bauer和Golinelli（2001）以及Enriquez和Menard（2016）的两种组合方法，并通过计数覆盖树的行走来近似谱测度的矩。