|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.
|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.
- 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.
- Parallel queues with synchronization, with O. Ruiz-Lacedelli. (2014) (Submitted), ArXiv:1501.00186 pdf
- Coupling on weighted branching trees, with N. Chen. (2014) (Submitted), ArXiv:1410.1050 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)
- 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:
- Efficient simulation of 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.