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Explore a technical lecture from MIT's Yury Polyanskiy examining recent developments in q-ary stochastic block model and broadcasting on trees (BOT). Delve into the mathematical analysis of uniqueness in distribution recursions and its implications for limiting mutual information between graph and community labels. Learn how uniqueness holds universally for q=2 cases, while q>2 scenarios currently show uniqueness only above specific thresholds approaching Kesten-Stigum bounds. Examine the relationship between BOT reconstruction and Kesten-Stigum thresholds, including cases involving vertex-level side information. Discover extensions to the Janson-Mossel 2004 robust reconstruction result, presented through collaborative research with Princeton's Qian Yu and MIT's Yuzhou Gu.
