Shankar Bhamidi receives an NSF grant to study random tree models and applications

Professor Shankar Bhamidi receives an NSF grant to study structural properties of random tree models and their applications in various fields including network flows and statistical physics.

Over the last few years the availability of empirical data on many real world networks including social networks, data transmission networks such as the Internet and various biological networks, has stimulated an explosion in the array of mathematical models proposed to understand these networks. Researchers in a wide array of fields are interested in understanding properties of such networks, the evolution and change of such networks over time, as well as the dynamics of various processes on these networks such as transporting flow or traffic through these networks and epidemic models on these networks. An understanding of the behavior of these mathematical models would allow practitioners to glean important information and insight about such processes in the real world, ranging from the design of more efficient networks, understanding the factors that influence the rate of spread of congestion of flow processes or other dynamics through the network, to the significant factors that contribute to the actual emergence of the structure of the network itself. A mathematical analysis of such problems leads to interesting connections between these models and wide areas of mathematical probability including branching process models in biology and random fractals.  The aim of this project is to develop mathematical methodology to understand properties of such network models and in particular understand what happens when the system size grows large.