Dr. Luca Avena
Niels Bohrweg 1
2333 CA Leiden
Email: l.avena at math.leidenuniv.nl
Luca Avena’s research activity is in probability theory with a focus on problems coming from statistical physics and network science, related to the theory of so called random walks and disordered media. Fundamental interests are on the rigorous analysis of models of random motion in non homogeneous networks with possibly random space-time features. From a more applied side, he has been recently active in developing randomized exploration algorithms for network data sets using random walks and related random combinatorial objects such as rooted spanning trees and forests. Both these fundamental and more applied lines of investigation heavily rely on a deep understanding of the delicate interplay between the behaviour of Markovian dynamics on a given graph and the spectral properties of the associated adjacency and Laplacian matrices.
A possible topic for a PhD project is to clarify some aspects of this delicate interplay by looking at scaling properties of spectra associated with key complex network models. Mathematical techniques that will be used come from probability theory, combinatorics and functional analysis. The PhD projects will be co-supervised by Frank den Hollander and Rajat Hazra (Leiden University).