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...