Concentration of the spectral norm of Erdös-Rényi random graphs

Seminar: Probability Seminar | September 5 | 3-4 p.m. | 1011 Evans Hall

 Gabor Lugosi, Pompeu Fabra University

 Department of Statistics

In this joint work with Shahar Mendelson and Nikita Zhivotovsky, we study concentration properties of the largest eigenvalue of the
adjacency matrix of a G(n,p) random graph. We use inequalities for higher moments of general functions of independent random variables and delocalization of the eigenvectors to prove nonasymptotic
concentration inequalities. In particular, we prove that the largest eigenvalue is uniformly concentrated for the entire random graph