Limit Theorem for Spectra of Laplace Matrix of Random Graphs

Abstract

We consider the limit of the empirical spectral distribution of Laplace matrices of generalized random graphs. Applying the Stieltjes transform method, we prove under general conditions that the limit spectral distribution of Laplace matrices converges to the free convolution of the semicircular law and the normal law.

Keywords

• semicircular law
• random graph
• normal law
• Stieltjes transform
• Laplace matrix