### Biography

Professor Olvera-Cravioto obtained her BS in Applied Mathematics from ITAM, in Mexico City, and her PhD in Management Science & Engineering from Stanford University; she also holds a MS in Statistics from Stanford University. She was a faculty in the Department of Industrial Engineering and Operations Research at Columbia University from 2006 until 2016. Her research interests are in Applied Probability, in particular, the asymptotic analysis of heavy-tailed phenomena. Her current work is focused on the analysis of information ranking algorithms and their large-scale behavior, which is closely related to the study of stochastic branching recursions. She is also interested in the analysis of power-law graphs (e.g. social networks) and queueing networks with parallel servers such as those encountered in cloud computing platforms. She is an Associate Editor for Stochastic Models and QUESTA.

### Research

**Stability of directed networks:**Random graphs are used to model real-world complex networks that are either too large to be analyzed directly or can be constantly changing. They are also very useful for determining whether a real graph is likely to have certain properties, such as short distances between vertices or large connected components. For directed graphs, the connectivity properties are a bit more subtle than in the undirected case, however, it is known that for several popular random graph models there is a threshold that determines whether there will exist a strongly connected component containing a positive fraction of all the vertices in the graph. The project I have in mind consists in analyzing a couple of models to try to determine how stable the size of the strongly connected component is with respect to the addition/removal of arcs. Closely related to this question, is whether typical distances between vertices remain stable under the same type of perturbations.

**Inversion methods for the computation of solutions to distributional equations:**Distributional fixed-point equations appear in a wide range of problems in operations research, computer science, mathematics, statistical physics, etc. In particular, many interesting problems lead to fixed-point equations that live on weighted trees, and the goal is to compute the distribution of one solution in particular. However, the exploding nature of trees makes the implementation of standard numerical methods very difficult, creating the need more efficient approaches. Some of my prior work includes the analysis of a Monte Carlo algorithm, known as “population dynamics”, that in many cases provides an efficient and accurate method. Unfortunately, it does not work under some ill-behaved but rather important settings, and for those cases we still need to find an efficient method. The project involves looking into Laplace inversion techniques to provide an alternative that works when the population dynamics algorithm fails.

I am currently looking for PhD students to work on problems related to these two themes. If you are interested, please send me an email to molvera@berkeley.edu.

### Publications

*On a family of inhomogeneous random digraphs*, with J. Cao. (2017) (Submitted) ArXiv:1712.03319 pdf*Likelihood Ratio Gradient Estimation for Steady-State Parameters*, with P. Glynn. (2017) ArXiv:1707.02659 pdf*PageRank on inhomogeneous random digraphs*, with J. Lee. (2017) (Submitted), ArXiv:1707.02492 pdf*Convergence of the Population Dynamics algorithm in the Wasserstein metric*. (2017) (Submitted) ArXiv:1705.09747 pdf*Parallel queues with synchronization*, with O. Ruiz-Lacedelli. (2014) (Submitted), ArXiv:1501.00186 pdf*Joint Audit and Replenishment Decisions for an Inventory System with Unrecorded Demands*, with T. Huh and O. Ozer. (Submitted)*Distances in the directed configuration model*, with P. van der Hoorn. (2015) To appear in Annals of Applied Probability, ArXiv:1511.04553 pdf*Generalized PageRank on directed configuration networks*, with N. Chen and N. Litvak. (2017) Random Structures and Algorithms, Vol. 51, No. 2, pp. 237-274. pdf*Efficient simulation for branching linear recursions*, with N. Chen. (2015) Proceedings of the Winter Simulation Conference 2015, pp. 2716-2727. pdf*Coupling on weighted branching trees*, with N. Chen. (2016) Advances in Applied Probability, Vol. 48, No. 2, pp. 499 - 524. 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