Loading Events

« All Events

  • This event has passed.
:

Joonkyung Lee (이준경), Majority dynamics on sparse random graphs

October 12 Tuesday @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

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 $p=\omega(1/n)$.

This 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 $\lambda’>0$.

Joint work with Debsoumya Chakraborti, Jeong Han Kim and Tuan Tran.

Details

Date:
October 12 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:
,

Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum (엄상일)
View Organizer Website
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
Copyright © IBS 2018. All rights reserved.