Author

Wen Sun

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Preprint Aug 2026

Uniform High Order Factorial Moment Bounds for the Critical Erd\H{o}s-R\'enyi Component Process

We give a finite $n$ enumerative derivation of the local surplus marked point process form of Aldous's critical window limit for the Erd\H{o}s-R\'enyi random graph. For $p_n=n^{-1}+\lambda n^{-4/3}$, let $\Xi_n$ place an atom at the rescaled size and surplus of each component. Exact component enumeration yields the lim...

Wen Sun · 0 citations

Preprint Jul 2026

Dynamical Equations for Poisson Galton--Watson Trees and Component Densities of Sparse Inhomogeneous Random Graphs

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 derivative between two parameter values and show that it remains measurable after projection to the total progeny measure. Under a uniform b...

Bohan Hu, Wen Sun · 0 citations