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math.PR2025
Decoupling of clusters in independent sets in a percolated hypercube
Mriganka Basu Roy Chowdhury, Shirshendu Ganguly, Vilas Winstein
Independent sets in graphs are sets of vertices containing no neighbors, and they represent a canonical spin system with hardcore constraints. Of particular interest is the setting…
math.PR2025
Quantitative central limit theorems for exponential random graphs
Vilas Winstein
Ferromagnetic exponential random graph models (ERGMs) are nonlinear exponential tilts of Erdős-Rényi models, under which the presence of certain subgraphs such as triangles may be…
math.PR2025
Concentration via metastable mixing, with applications to the supercritical exponential random graph model
Vilas Winstein
Folklore belief holds that metastable wells in low-temperature statistical mechanics models exhibit high-temperature behavior. We make this rigorous in the exponential random graph…