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The aim of this talk is to describe the role of long range dependence in the evolution of dynamic network models, to understand the role of this phenomenon in classical change point detection techniques as well as in the identification of the root or originator of the network.
a) We will consider models of evolving networks where the dynamics modulating the evolution change after some point in time. We will describe (in the context of models such as preferential attachment) long range dependence of the initial segment of the network on the evolution of the network and its role in proposing change point detection.
b) Suppose we are given a growing random tree modulated by some growth dynamics started from an initial seed graph. Suppose after some large time we are given access only to the topology of the tree with no knowledge of the time or order of entry of various individuals in the tree and our goal is to estimate the initial seed graph. In this setting one can take advantage of long range dependence to formulate functionals of the network that remain persistent over time.
This work is largely done with Sayan Banerjee at UNC and Iain Carmichael (U of W).
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