Research of the spectrum of the very sparse random matrices

Firstly, the concept of the sparse and very sparse matrices was introduced in this thesis. The methods used in very sparse matrices theory were thoroughly studied and the results were illustrated by examples. The analysis also focused on the selection method for very sparse random matrices. This method is used to show that the limit of expected spectral distribution function has a discrete part. New points of discontinuity of the spectral distribution function were found with the help of this method. Furthermore, the length on the discontinuity jump were specified in some of the found discontinuity points. The examination revealed if there was a particular way to select matrices, which would prove that the limit of the spectral distribution function has an absolutely continues part