Mariana Olvera-Cravioto
Associate Professor

Industrial Engineering and Operations Research
Columbia University

306 S. W. Mudd Building
500 W. 120th Street
New York, New York 10027

Phone: (212) 854 4703
Fax: (212) 854 8103

Email: molvera@ieor.columbia.edu

Mini Bio
I was born in Mexico City, and lived there until 2001, when I came to the United States to start my doctoral studies. My bachelor's degree is in Applied Mathematics from the "Instituto Tecnológico Autónomo de México (ITAM)", and I hold a master's degree on Statistics from Stanford University. I obtained my PhD from the Department of Management Science and Engineering at Stanford University, where I worked on problems related to the single-server queue with heavy-tailed processing times.

I joined Columbia University in the fall of 2006. I teach courses at all three levels (undergraduate, master's, and doctoral) in the stochastic area of the department. Besides research, I am always happy to talk about classical music, swimming, biking, Mexico and the many wonderful things it has to offer.


Research
interests
My research interests are in Applied Probability, in particular, in asymptotic analysis involving heavy-tailed distributions. My current work is focused on the analysis of information ranking algorithms and their large-scale behavior, which is closely related to the study of the asymptotic properties of solutions to certain stochastic recursions, in particular, weighted branching processes. I am also interested in the analysis of queueing networks with parallel servers such as those encountered in cloud computing platforms. Other areas that interest me are stochastic processes, queueing theory, power-law graphs (e.g. social networks), large deviations and simulation.


Teaching
Spring 2014-15:
  • SIEO 3600, Introduction to Probability and Statistics. This is an introductory course on probability and statistics for undergraduates.
    Lectures: Mondays, Wednesdays, 11:40 am - 12:55 pm, S.W. Mudd 833
  • IEOR 4106, Intro to OR: Stochastic Models. This is a master level course on stochastic models. Topics include: the Poisson process, renewal theory, discrete and continuous time Markov chains.
    Lectures: Mondays, Wednesdays, 1:10 - 2:25 pm, S.W. Mudd 633

Course information and materials available to registered students via CourseWorks.
A list of previously taught courses can be found here
.


Publications
Publications:
  • Parallel queues with synchronization, with O. Ruiz-Lacedelli. (2014) (Submitted), ArXiv:1501.00186 pdf
  • Ranking algorithms on directed configuration networks, with N. Chen and N. Litvak. (2014) (Submitted), ArXiv:1409.7443 pdf
  • Joint Audit and Replenishment Decisions for an Inventory System with Unrecorded Demands, with T. Huh and O. Ozer. (Submitted)
  • Efficient simulation for branching linear recursions, with N. Chen. (2015) To appear in Proceedings of the Winter Simulation Conference 2015, ArXiv:1503.09150 pdf
  • Coupling on weighted branching trees, with N. Chen. (2014) To appear in Advances in Applied Probability, Vol. 48, No. 2, ArXiv:1410.1050 pdf
  • Maximums on Trees, with P. Jelenkovic. (2015) Stochastic Processes and their Applications, Vol. 125, pp. 217-232 pdf
  • PageRank in scale-free random graphs, with N. Chen and N. Litvak. (2014) Proceedings of the 11th Workshop on Algorithms and Models for the Web Graph, Beijing, China, December 2014. pdf
  • Directed Random Graphs with Given Degree Distributions, with N. Chen. (2013) Stochastic Systems, Vol. 3, No. 1, pp. 147-186. pdf.
  • Convergence rates in the Implicit Renewal Theorem on Trees, with P. Jelenkovic. (2013) Journal of Applied Probability, Vol. 50, No. 4, pp. 1077-1088. pdf.
  • Power Laws on Weighted Branching Trees, with P. Jelenkovic. (2013) Random Matrices and Iterated Random Functions, Springer Proceedings in Mathematics and Statistics, 53: 159-187. pdf.
  • Asymptotics for Weighted Random Sums. (2012) Advances in Applied Probability, Vol. 44, No. 4, pp. 1142-1172. pdf.
  • Implicit Renewal Theorem for Trees with General Weights, with P. Jelenkovic. (2012) Stochastic Processes and their Applications, Vol. 122, No. 9, pp. 3209-3238. pdf.
  • Tail behavior of solutions of linear recursions on trees. (2012) Stochastic Processes and their Applications, Vol. 122, No. 4, pp. 1777-1807. pdf.
  • Implicit Renewal Theory and Power Tails on Trees, with P. Jelenkovic. (2012) Advances in Applied Probability, Vol. 44, No. 2, pp. 528-561. pdf.
  • Uniform Approximations for the M/G/1 Queue with Subexponential Processing Times, with P. Glynn. (2011) Queueing Systems. Vol. 68, No. 1, pp. 1-50. pdf.
  • On the Transition from Heavy Traffic to Heavy Tails for the M/G/1 Queue: The Regularly Varying Case, with J. Blanchet and P. Glynn. (2011) Annals of Applied Probability. Vol. 21, No. 2, pp. 645-668. pdf. Internet supplement pdf.
  • Information ranking and power laws on trees, with P. Jelenkovic. (2010). Advances in Applied Probability. Vol. 42, No. 4, pp. 1057-1093. Short version pdf. Long version pdf.
  • On the distribution of the nearly unstable AR(1) process with heavy-tails. (2010). Advances in Applied Probability. Vol. 42, No. 1, pp. 106-136. pdf.

Work in progress:

  • Strongly consistent estimators for solutions to branching recursions, with N. Chen.
  • Model Robustness of Tail Distributions, with P. Glynn.
  • Gradient Estimation of Steady State Parameters via Likelihood Ratios, with P. Glynn.
  • Distances in the directed configuration model, with P. van der Hoorn.

Data sets: