Kavita Ramanan

Professor
Ph.D., Brown University

Office: Wean Hall 6204
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.