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arXiv · 1303.0050

Tracking the Empirical Distribution of a Markov-modulated Duplication-Deletion Random Graph

Maziyar Hamdi·Vikram Krishnamurthy·George Yin
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Abstract

This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite state Markov chain. The paper comprises of 2 results. First, motivated by social network applications, we analyze the asymptotic behavior of the degree distribution of the Markov-modulated random graph. Using the asymptotic degree distribution, an expression is obtained for the delay in searching such graphs. Second, a stochastic approximation algorithm is presented to track empirical degree distribution as it evolves over time. The tracking performance of the algorithm is analyzed in terms of mean square error and a functional central limit theorem is presented for the asymptotic tracking error.

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Maziyar Hamdi, Vikram Krishnamurthy, George Yin. 2013-02-28. Tracking the Empirical Distribution of a Markov-modulated Duplication-Deletion Random Graph. https://arxiv.org/abs/1303.0050

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