YEP XVIII — Spectra of random graphs and related combinatorial problems

The study of matrices with random entries started in the 1950’s and has grown into an immense body of literature until today. While the initial focus was on problems in statistical physics, in recent times random matrices have proven to be an important tool also in a variety of other fields like statistics, network analysis, image processing or machine learning. Moreover, there has been great progess in the study of matrices which arise naturally in random graphs, like the adjacency matrix, the Laplacian matrix, or the transition matrix of the random walk on the graph. The recent theoretical advances in this area are remarkable and one of the key goals of the workshop is to understand the information contained in eigenvalues and eigenvectors of high-dimensional random matrices. A second point of focus are applications of tools stemming from random graphs theory that can be used to study the spectrum of random matrices. In this workshop, we provide a platform where young and more senior researchers from the area of random matrices, random graphs and related topics can come together and exchange their research, find new collaborations and learn about different perspectives on the topic.