Faculty
Visiting Faculty
Staff
Graduate Students
Home
|
|
 Kavita Ramanan
Associate Professor
Ph.D., Brown University
Office: Wean Hall 6208
Phone: (412) 268-8485
E-mail: kramanan AT math.cmu.edu
Research
Kavita Ramanan's research
lies in the area of probability theory,
stochastic processes and their applications. A focus of her work has been
on the theory of reflected diffusions and large deviations and
their applications to the analysis of stochastic networks. Other areas
of interest include the study of Gibbs measures and phase transitions,
stochastic control and random perturbations of dynamical systems.
She was a member of the Mathematical Sciences Center at Bell Laboratories,
NJ, for several years prior to joining Carnegie Mellon University. As a
result her work has enjoyed a symbiotic relationship with applications --
in particular the design, performance analysis and control of
communication networks. The consideration of concrete practical
problems often gives rise to interesting fundamental mathematical
questions, the solution of which sheds insight into a larger class
of problems than originally intended.
Selected Publications
K. Ramanan and M. Reiman, ``Fluid and heavy traffic limits of a
generalized processor sharing model'', Ann. of App. Prob., 13, 1:100--139, 2003.
P. Dupuis and K. Ramanan, ``A time-reversed representation for
the tail probabilities of reflected Brownian motion'', Stoch. Proc. and their App., 98 2:253--287, 2002.
K. Ramanan, A. Sengupta, I. Ziedins and P.\Mitra,
``Markov Random Field Models of Multicasting in Tree Networks'', Adv. in App. Prob., 34 1:1--27, 2002.
K. Ramanan and O. Zeitouni, ``The quasi-stationary distribution
for small random perturbations of certain one-dimensional
maps'', Stoch. Proc. and their App., 84 25--51, 1999.
P. Dupuis and K. Ramanan, ``Convex Duality and the Skorokhod Problem -
Parts I and II'', Prob. Theory and Rel. Fields, 115 2:153--236, 1999.
|
