The goal of the project is to study spectra of the adjacency matrices of random graphs. For Erdos-Renyi random graphs the adjacency matrix is a generalised Wigner matrix where the entries are independent Bernoulli random variables with the same success probability. For inhomogeneous Erdos-Renyi random graphs the success probabilities are not same. The literature on spectra of random graphs for which the success probabilities are dependent is very limited. The project aims to explore what can be said for such random graphs, which include uniform random graphs, configuration models and preferential attachment models. Relevant statistics of the spectrum include the limiting spectral measure, the spectral norm and the spectral gap. Most techniques in random matrix theory rely on weak dependence of the entries and so a significant improvement is needed to deal with strong dependence.
|Supervisors||Rajat Hazra (UL), Luca Avena (LU) and Frank den Hollander (LU)|
|PhD Student||Nandan Malhotra|