Spectra, Algorithms and Random Walks on Random Networks
The theory of random graphs is a field in evolution. Since its beginning at the end of the fifties until the present day, these random discrete structures have been increasingly used in mathematics and, more broadly, in computer science, in physics, biology and the social sciences. They are commonly employed to model large complex networks and disordered lattices. They are also used in the design of algorithms and to prove the existence of sophisticated combinatorial structures. Their popularity comes from the fact that they have proved to be both versatile and propitious to analytical study. This activity has generated a number of exciting new mathematical questions. These questions are offundamental importance to understanding the subtle interplay between the geometry of the graph and the processes defined on it. A vast research effort is notably devoted to the rigorous understanding of the properties of spectra, random walks and spectral algorithms defined on random graphs. These three objects are closely related and they are at the core of both theoretical and more applied issues. They range from wave propagation in disordered media to community detection in social networks.
