4 papers
Majority Dynamics on Resampled Sparse Erdős--Rényi Graphs: Gaussian Winner Selection and Pace to Unanimity
Ioana Dumitriu, Muchen Ju, Hai-Xiao Wang
We study the two-opinion majority dynamics process: at each time step, every vertex adopts the majority opinion among its neighbors, retaining its current opinion if there is a tie…
Majority Dynamics on Assortative Sparse Stochastic Block Models
Ioana Dumitriu, Muchen Ju, Hai-Xiao Wang
Majority dynamics is a two-opinion process in which each vertex repeatedly updates to the majority opinion among its neighbors. We study this process on a resampled sparse binary s…
Sharp Inner Product Correlations for Hypercube Bijections
Ijay Narang, Muchen Ju
We resolve a conjecture of Rob Morris concerning bijections on the hypercube. Specifically, we show that for any bijection , \[ \Pr_{x,y \in \{-1,1\}…
Arborescences of Random Covering Graphs
Muchen Ju, Junjie Ni, Kaixin Wang +1
A rooted arborescence of a directed graph is a spanning tree directed towards a particular vertex. A recent work of Chepuri et al. showed that the arborescences of a covering graph…