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DTSTART;TZID=Asia/Seoul:20211012T163000
DTEND;TZID=Asia/Seoul:20211012T173000
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UID:4374-1634056200-1634059800@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, Majority dynamics on sparse random graphs
DESCRIPTION:Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini\, Chan\, O’Donnell\, Tamuz and Tan conjectured that\, in the Erdős-Rényi random graph $G(n\,p)$\, the random initial $\pm 1$-assignment converges to a $99\%$-agreement with high probability whenever $p=\omega(1/n)$. \nThis conjecture was first confirmed for $p\geq\lambda n^{-1/2}$ for a large constant $\lambda$ by Fountoulakis\, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin\, it was unknown whether the conjecture holds for $p< \lambda n^{-1/2}$. We break this $\Omega(n^{-1/2})$-barrier by proving the conjecture for sparser random graphs $G(n\,p)$\, where $\lambda’ n^{-3/5}\log n \leq p \leq \lambda n^{-1/2}$ with a large constant $\lambda’>0$. \nJoint work with Debsoumya Chakraborti\, Jeong Han Kim and Tuan Tran.
URL:https://dimag.ibs.re.kr/event/2021-10-12/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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