2 papers
math.PR2026
Uniform High Order Factorial Moment Bounds for the Critical Erdős-Rényi Component Process
Wen Sun
We give a finite enumerative derivation of the local surplus marked point process form of Aldous's critical window limit for the Erdős-Rényi random graph. For $p_n=n^{-1}+λn^{-…
math.PR2026
Dynamical Equations for Poisson Galton--Watson Trees and Component Densities of Sparse Inhomogeneous Random Graphs
Bohan Hu, Wen Sun
We study Poisson Galton--Watson trees on a standard Borel type space when the offspring kernel is multiplied by a scalar parameter. On finite trees, we identify the Radon--Nikodym…