Random graphs and complex networksIn the past two decades, it has become clear that many real networks share fascinating features in being small worlds and scale-free. Such networks are typically modeled using random graphs. Random graphs are closely related to percolation, the difference being that random graphs tend to have finite size, while percolation systems tend to be infinite. The empirical findings on real networks have ignited research on various models for complex networks. The focus of the research of the group was the study of distances in models of complex networks where power-law degrees are observed, as well as the behavior of stochastic processes on random graphs.
Percolation and high-dimensional statistical physicsPercolation is one of the paradigm models in statistical physics, displaying extremely rich critical behavior. It is a model of a porous medium, where the materials consist of substance and holes. My main focus of research in the past period has been on the study of percolation models close to criticality for high-dimensional systems. Related problems include lattice trees and lattice animals, and the Ising model, in high-dimensions.
MethodologyIn this research, we mainly make use of four key methods:
Applications of ProbabilityI have always been interested in applications of probability, particularly in electrical engineering, computer science and theoretical physics. So if you have a cool problem, please knock on my door!