Meetings of random walks & consensus dynamics on sparse random digraphs.

I will first discuss the general relation between meeting time of random walks and consensus time in Markovian opinion dynamics on finite networks. I will then focus on sparse random directed graphs and give an account on a recent result in which we characterize how random walks meet in such directed setup and related implications for opinion dynamics. I will in particular discuss how the directed degree structure of the underlying network may speed up or slow down meetings of different random walks.

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