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arXiv:1303.0050 [cs.IT]AbstractReferencesReviewsResources

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

Maziyar Hamdi, Vikram Krishnamurthy, George Yin

Published 2013-02-28Version 1

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.

Comments: 34 pages, 8 figures, submitted to IEEE Transactions on Information Theory
Categories: cs.IT, math.IT
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