# 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.