Speaker: Jules Morand.

Abstract: Stochastic processes evolving on graphs are used to model a variety of phenomena, ranging from search algorithms and the spreading of infections, damages, attacks, or rumors, to the detection of communities in social networks. In these applications the focus is generally on averaged quantities such as mean first-passage times. Much less is understood about the occurrence of rare events or fluctuations far away from average or typical values, related, for example, to the rapid spreading of a disease in a dispersed population. I will present in this talk, a recently published work, which study the large deviations of time integrated observables of an unbiased random walk evolving on Erdös-Rényi random graphs. I will show, in the case where the observable the sum of the degrees visited, how to construct a modified, biased random walk, that explains how these fluctuations arise in the long-time limit. The biased random walk, or driven process, can also be controlled to identify nodes with low or high degree, or other graph properties, without knowing the detailed structure of the graph.

Short bio: Jules Morand is presently a post-doctoral researcher in the Physics of Biological Systems group at BioISI (Biosystems and Integrative Science Institute), Universidade de Lisboa. His current research on computational biophysics is focused on the mechanisms of protein folding and aggregation. Previously, he did his PhD at LPNHE (Paris), under supervision of  M. Joyce, cosmologist specialist on structure formation and long-range interacting systems, and P. Viot former director of LPTMC (Paris), an expert in granular matter and computational physics. Afterwards, he worked at the University of Stellenbosch (South Africa) with H. Touchette, an expert  on diffusion phenomena and Large Deviation Theory.