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When Markov chains meet: a continuous-time model of network evolution. (English) Zbl 1343.60114

Summary: We suggest a novel approach to model continuous time processes of the interactions of independent elements. The model assumes a finite number of independent Markov chains, each representing an element. Chains move among a common space of states. Sometimes chains intersect, being in the same state at the same time. These intersections relate the chains with each other and imply many interesting processes. In this paper, we examine our new approach in the context of network evolution. Our analytic study achieves a closed solution for the expected time until a node has any specific degree. Our numerical study demonstrates properties which are in agreement with real world networks. Thus we show the potential of our approach.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60J28 Applications of continuous-time Markov processes on discrete state spaces
60K35 Interacting random processes; statistical mechanics type models; percolation theory
90B15 Stochastic network models in operations research
65C40 Numerical analysis or methods applied to Markov chains
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