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math.PR2026
Perron--Wright asymptotics and critical component processes for inhomogeneous random graphs
Wentao Hu, Wen Sun
We extend Wright's enumeration of connected labelled graphs with fixed surplus to irreducible critical finite type kernels and continuous compact type kernels satisfying a positivi…
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…