Speaker: Artem Ryabov, Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics

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: Artem Ryabov is currently an assistant professor at the Faculty of Mathematics and Physics at Charles University, Prague, Czech Republic. He was born in Moscow, USSR, 1985, and in 1998 he moved with family to the Czech Republic. As an undergraduate Artem studied General Physics at Charles University, graduated in Physics of Condensed Matter and Materials (2010, Mgr. degree, Charles University), and in 2014 he obtained PhD degree in Biophysics, Chemical and Macromolecular Physics, at Charles University in Prague. His thesis "Stochastic Dynamics and Energetics of Biomolecular Systems", adviser: Prof. Petr Chvosta, has been recognized as an outstanding by Springer and published is Springer Theses series. After PhD, Artem started to work in a theory group of the Department of Macromolecular Physics, developing his research interests with a focus on theoretical biophysics and soft matter physics, non-equilibrium statistical mechanics, and stochastic thermodynamics.