QUESTIONS, METHODS & CONNECTIONS
Research
Understanding structure in random networks.
My interests lie at the intersection of random graph theory, probability, statistical inference, and structural control theory, with connections to signal processing.
Graphons & random graph structure
Graphons provide a way to describe large random networks through a limiting object. I study when graphs sampled from step-graphons admit cycle covers, and how this behavior is encoded by the underlying graphon.
My work on the H-property focuses on the residual case: a boundary regime in which the limiting probability can lie between zero and one. With Xudong Chen, I characterize this limit and study its geometric structure.
Convergence rates & asymptotic probability
Limit theorems tell us what happens as a network grows. Convergence rates tell us how quickly the limiting description becomes informative.
With Hong Hu and Xudong Chen, I study the rate at which cycle-cover probabilities converge for step-graphons. Our work identifies exponential and root-n regimes, connecting the geometry of graphons with probabilistic asymptotics.
Statistical inference in noisy networks
I am also interested in recovering latent network structure when observations are imperfect. Questions include estimating edges and community labels, understanding the information available in repeated observations, and analyzing iterative inference algorithms.
Topics: stochastic block models, message passing, and approximate message passing.
Earlier work
My earlier research explored multi-turn dialogue agents for telemarketing assistance, presented at IJCNN 2023.