Abstract
AbstractWe analyze the asynchronous version of the DeGroot dynamics: In a connected graph with nodes, each node has an initial opinions in and an independent Poisson clock. When a clock at a node rings, the opinion at is replaced by the average opinion of its neighbors. It is well known that the opinions converge to a consensus. We show that the expected time to reach ‐consensus is poly in undirected graphs and in Eulerian digraphs, but for some digraphs of bounded degree it is exponential. Our main result is that in undirected graphs and Eulerian digraphs, if the degrees are uniformly bounded and the initial opinions are i.i.d., then for every fixed . We give sharp estimates for the variance of the limiting consensus opinion, which measures the ability to aggregate information (“wisdom of the crowd”). We also prove generalizations to non‐reversible Markov chains and infinite graphs. New results of independent interest on fragmentation processes and coupled random walks are crucial to our analysis.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
