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The common measure reached at each agent is one minimizing a weighted sum of its Wasserstein distance to all initial agent measures. This measure is known as the Wasserstein barycenter. Special cases involving Gaussian measures, empirical measures, and time-invariant network topologies are considered, where convergence rates and average-consensus results are given. This work has possible applicability in computer vision, machine learning, clustering, and estimation.<\/jats:p>","DOI":"10.1137\/19m1268252","type":"journal-article","created":{"date-parts":[[2021,9,21]],"date-time":"2021-09-21T10:48:51Z","timestamp":1632221331000},"page":"3261-3277","source":"Crossref","is-referenced-by-count":5,"title":["Network Consensus in the Wasserstein Metric Space of Probability Measures"],"prefix":"10.1137","volume":"59","author":[{"given":"Adrian N.","family":"Bishop","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnaud","family":"Doucet","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,9,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1974.10480137"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1986.1104412"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.812781"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.834113"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.841888"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.846556"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2006.887293"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/060657005"},{"key":"atypb9","first-page":"63","author":"Xiao L.","year":"2005","journal-title":"Los Angeles, IEEE"},{"key":"atypb10","unstructured":"D.P. 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