5 papers
Coefficient Positivity for Arborescence Ratios of Covering Digraphs
Muchen Ju, Junjie Ni, Kaixin Wang +1
For a directed graph with a chosen root, the arborescence polynomial sums the products of edge weights over all spanning trees directed toward that root. In a finite graph cover, e…
Majority Dynamics on Resampled Sparse Erdős--Rényi Graphs: Gaussian Winner Selection in Collaborative Agent Networks
Ioana Dumitriu, Muchen Ju, Hai-Xiao Wang
Collective decisions in agent networks emerge from repeated local interactions, as agents update their opinions (colors) based on their neighbors, potentially leading to consensus.…
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…