3
$\begingroup$

Particularly, I am dealing with Erdős–Rényi random 𝐺(𝑛,𝑝), so the expected Laplacian matrix of 𝐺(𝑛,𝑝) is 𝑝(𝐽𝑛−𝐼𝑛), where 𝐽𝑛 and 𝐼𝑛 are one and identity matrices, respectively.

In addition,if the distribution (unsure, but might be power law) of the eigenvalues of Laplacian matrix of the graph 𝐺(𝑛,𝑝) is known, then it seems to me that expected value of the eigenvalues has some closed form formula depending on 𝑛 and 𝑝 in the asymptotic case.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

See the papers by Erdos (no relation) and collaborators, e.g.:

Erdős, László; Knowles, Antti; Yau, Horng-Tzer; Yin, Jun, Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law, Ann. Probab. 41, No. 3B, 2279-2375 (2013). ZBL1272.05111.

Erdős, László; Knowles, Antti; Yau, Horng-Tzer; Yin, Jun, Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues, Commun. Math. Phys. 314, No. 3, 587-640 (2012). ZBL1251.05162.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .