The IV AMMCS International Conference
Waterloo, Ontario, Canada | August 20-25, 2017
AMMSCS 2017 Plenary Talk
Scaling Limits of Stochastic Networks
Kavita Ramanan (Brown University)
Stochastic networks arise in a variety of applications, ranging from communication and service networks to biochemical reaction networks. In many cases, these networks are too complex to be amenable to an exact analysis, and so it is useful to identify tractable approximations that provide qualitative insight into the dynamics, and whose accuracy can be rigorously justified via limit theorems in a suitable asymptotic regime. This talk will provide a survey of mathematical methods that have been developed to identify and analyze these scaling limits in different settings, and the qualitative insight they provide into network performance and design. We will also provide some illustrative examples of how the mathematical tools developed to analyze stochastic networks have been applied in other areas of probability, for the study of interacting particle systems, random matrices, and models in math finance.
Kavita Ramanan is a professor at the Division of Applied Mathematics at Brown University. She previously held positions as professor of mathematics at Carnegie Mellon University and a Member of Technical Staff at Bell Laboratories. Her research lies in the area of probability theory, stochastic processes and their applications, including stochastic analysis, high-dimensional probability, large deviations, and applications to stochastic networks. She was awarded the Erlang Prize for outstanding contributions to applied probability by the INFORMS Applied Probability Society in 2006, was elected a fellow of the IMS (Institute for Mathematics and Statistics) in 2013 and was awarded the IMS Medallion in 2015. She has served on the editorial boards of several journals, including the Annals of Probability, Annals of Applied Probability, Queueing Systems and Stochastic Analysis and Applications, and is currently the Area Editor of Mathematics of Operations Research. She is the faculty founder of the AWM student chapter at Brown University and also runs a math outreach group at Brown called the Math CoOp.