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math.PR2026
Concentration of Regularized Sparse Random Matrices: Spectral Edge Bounds via Nonbacktracking Operators
Hai-Xiao Wang
In sparse random matrices, spectral outliers (eigenvalues and singular values located away from the bulk) emerge due to degree fluctuations: high degrees inflate the operator norm,…
math.PR2026
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.…
math.PR2026
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…