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Mini Bio
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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 September 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.
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Research
interests
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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. Other areas that interest me are large deviations, stochastic processes, queueing theory, power-law graphs (e.g. social networks) and simulation.
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Teaching
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Spring 2011-12:
- IEOR 4404, Simulation. This course covers the basics of discrete event simulation, and is intended for master's students and senior undergraduates with a good background in probability. A course on stochastic processes is recommended, but not a requirement.
Previous semesters:
- SIEO 3600, Introduction to Probability. This is an introductory course on probability and statistics for undergraduates.
- IEOR 3658, Probability. This is an introductory course on probability at the undergraduate level.
- IEOR 4404, Simulation. This course covers the basics of discrete event simulation, and is intended for master's students and senior undergraduates with a good background in probability. A course on stochastic processes is recommended, but not a requirement.
- IEOR 6711, Stochastic Models I. Advanced treatment of stochastic modeling in the context of queueing, reliability, manufacturing, insurance risk, financial engineering and other engineering applications. Review of elements of probability theory; exponential distribution; renewal theory; Wald's equation; Poisson processes. Introduction to both discrete and continuous-time Markov chains.
- IEOR 8100, Branching Processes and Applications. This is an introductory PhD-level course to the theory and applications of branching processes. The course is designed to build up from basic probability and stochastic processes, and is therefore suitable for first year PhD students or advanced master students interested in the topic. (Last taught in spring 2010-11)
- IEOR 8100, Large Deviations: Applications in OR. This is a PhD level course on large deviations with applications to queueing theory. (Last taught in spring 2007-08)
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Publications
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Publications:
- Implicit Renewal Theorem for Trees with General Weights, with P. Jelenković. (Submitted). arXiv:1012.2165, October 2011. pdf.
- Asymptotics for Weighted Random Sums. (Submitted). arXiv:1102.0301, February 2011. pdf.
- Joint Audit and Replenishment Decisions for an Inventory System with Unrecorded Demands, with T. Huh and O. Ozer. (Submitted)
- Tail behavior of solutions of linear recursions on trees. To appear in Stochastic Processes and their Applications. arXiv:1108.3809, August 2011. pdf.
- Implicit Renewal Theory and Power Tails on Trees, with P. Jelenković. To appear in Advances in Applied Probability, Vol. 44, No. 2. arXiv:1006.3295, October 2011. 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. Jelenković. (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:
- Model Robustness of Tail Distributions, with P. Glynn.
- Gradient Estimation of Steady State Parameters via Likelihood Ratios, with P. Glynn.
- On the transition from heavy traffic to heavy tails for the M/G/1 queue: the stable-law case, with G. Pang.
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