Filtering Random Graph Processes Over Random Time-Varying Graphs

Random Planar Structures and Random Graph Processes

Distributed Linear Filtering and Prediction of Time-varying Random Fields

We study distributed estimation of dynamic random fields observed by a sparsely connected network of agents/sensors. The sensors are inexpensive, low power, and they communicate locally and perform computation tasks. In the era of large-scale systems and big data, distributed estimators, yielding robust and reliable field estimates, are capable of significantly reducing the large computation an...

Exponential-Family Random Graph Models with Time Varying Network Parameters

Dynamic networks are a general language for describing time-evolving complex systems, and have long been an interesting research area. It is a fundamental research question to model time varying network parameters. However, due to difficulties in modeling functional network parameters, there is little progress in the current literature to effectively model time varying network parameters. In th...

Stochastic processes in random graphs

We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint distribution of the number of connected components, of the sizes of the giant components, and of the numbers of the excess edges of the giant components. For the sup...

Random and Quasirandom Graphs Lecture 2: Modeling a Random Graph

probability of this graph occurring is ( 1 2 )(n2), i.e. the same probability that we gave above in our probability space. Given this model, a natural sequence of questions to ask is “what properties is a random graph likely to have?” For example, consider counting the number of edges in a random graph, or triangle subgraphs, or connectivity, or other such properties: what should we expect thes...