SPEAKER:  Souvik Dhara  (Eindhoven)

TITLE:  Critical percolation on networks with given degrees

ABSTRACT: 

We discuss recent developments on the critical behavior of percolation on scale-free networks.  Scale-free networks are ubiquitous in real world arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental model for understanding robustness and spread of epidemics on these networks. We describe how the power-law exponent of the degree distribution governs the structural properties of the connected components. When the degree distribution has a finite third moment, the behavior turns out to be similar to the Erdos-Renyi random graph model, whereas the behavior for heavy-tailed networks with infinite third moment crucially depends on the hubs of very high degree. Furthermore, we explain how the clusters evolve dynamically when the percolation parameter ranges through the critical scaling window, eventually giving birth to the giant component in the supercritical phase with its inherently rich topological structure.

The talk is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden, and Sanchayan Sen.