The bulk of the random graph literature concerns models that are of an inherently static nature, in that features of the random graph at a single point in time are considered. There are strong practical motivations, however, to consider random graphs that are stochastically evolving, so as to model networks’ inherent dynamics.
In this talk I’ll discuss a set of dynamic random graph mechanisms and their probabilistic properties. Key results cover functional diffusion limits for sub graph counts (describing the behaviour around the mean) and a sample-path large-deviation principle (describing the rare-event behaviour, thus extending the seminal result for the static case developed by Chatterjee and Varadhan).
The last part of my talk will be about estimation of the model parameters from partial information. We for instance demonstrate how the model’s underlying parameters can be estimated from just snapshots of the number of edges. We also consider settings in which particles move around on a dynamically evolving random graph, and in which the graph dynamics are inferred from the movements of the particles (i.e., not observing the graph process).
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