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, at a larger scale, in computer science, in physics, biology or human 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 advanced 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 of fundamental importance to understand 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 the spectra, random walks and iterative propagation 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.
The objective of the project SAMARA is to contribute significantly to the mathematical understanding of these objects.
Monsieur Charles Bordenave (Centre National de la Recherche Scientifique Délégation Provence et Corse_Institut de Mathématiques de Marseille)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
IMT UNIVERSITE TOULOUSE III - Paul Sabatier
I2M Centre National de la Recherche Scientifique Délégation Provence et Corse_Institut de Mathématiques de Marseille
Help of the ANR 174,743 euros
Beginning and duration of the scientific project: December 2016 - 48 Months