
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 singleserver queue with heavytailed 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 heavytailed distributions. My current work is focused on the analysis of information ranking algorithms and their largescale 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, powerlaw graphs (e.g. social networks) and simulation.

Teaching

Fall 201415:
 IEOR 8100, Random Graphs. This is an introductory PhD level course on random graph theory. The topics will cover the classical ErdosRenyi, preferential attachment and configuration models, including some recent results and generalizations. We will discuss applications to social networks and the WWW, among others. A solid background in probability at the level of IEOR 4106 or higher is recommended.
Previous semesters:
 SIEO 3600, Introduction to Probability and Statistics. 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 continuoustime Markov chains.
 IEOR 8100, Branching Processes and Applications. This is an introductory PhDlevel 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 201011)
 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 200708)

Publications

Publications:
 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
 PageRank in scalefree random graphs, with N. Chen and N. Litvak. (2014) To appear in Proceedings of the 11th Workshop on Algorithms and Models for the Web Graph, Beijing, China, December 2014. ArXiv:1408.3610 pdf
 Maximums on Trees, with P. Jelenkovic. (2015) Stochastic Processes and their Applications, Vol. 125, pp. 217232, ArXiv:1405.6265 pdf
 Joint Audit and Replenishment Decisions for an Inventory System with Unrecorded Demands, with T. Huh and O. Ozer. (Submitted)
 Directed Random Graphs with Given Degree Distributions, with N. Chen. (2013) Stochastic Systems, Vol. 3, No. 1, pp. 147186. pdf.
 Convergence rates in the Implicit Renewal Theorem on Trees, with P. Jelenkovic. (2013) Journal of Applied Probability, Vol. 50, No. 4, pp. 10771088. pdf.
 Power Laws on Weighted Branching Trees, with P. Jelenkovic. (2013) Random Matrices and Iterated Random Functions, Springer Proceedings in Mathematics and Statistics, 53: 159187. pdf.
 Asymptotics for Weighted Random Sums. (2012) Advances in Applied Probability, Vol. 44, No. 4, pp. 11421172. pdf.
 Implicit Renewal Theorem for Trees with General Weights, with P. Jelenkovic. (2012) Stochastic Processes and their Applications, Vol. 122, No. 9, pp. 32093238. pdf.
 Tail behavior of solutions of linear recursions on trees. (2012) Stochastic Processes and their Applications, Vol. 122, No. 4, pp. 17771807. pdf.
 Implicit Renewal Theory and Power Tails on Trees, with P. Jelenkovic. (2012) Advances in Applied Probability, Vol. 44, No. 2, pp. 528561. pdf.
 Uniform Approximations for the M/G/1 Queue with Subexponential Processing Times, with P. Glynn. (2011) Queueing Systems. Vol. 68, No. 1, pp. 150. 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. 645668. pdf. Internet supplement pdf.
 Information ranking and power laws on trees, with P. Jelenkovic. (2010). Advances in Applied Probability. Vol. 42, No. 4, pp. 10571093. Short version pdf. Long version pdf.
 On the distribution of the nearly unstable AR(1) process with heavytails. (2010). Advances in Applied Probability. Vol. 42, No. 1, pp. 106136. pdf.
Work in progress:
 Queues with synchronization and parallel processing, with O. RuizLacedelli.
 Model Robustness of Tail Distributions, with P. Glynn.
 Gradient Estimation of Steady State Parameters via Likelihood Ratios, with P. Glynn.


