Prefer a chat interface with context about you and your work?
On the number of vertices with a given degree in a Galton-Watson tree
Let Y k (ω) ( k ≥ 0) be the number of vertices of a Galton-Watson tree ω that have k children, so that Z (ω) := ∑ k ≥0 Y k (ω) is the total progeny of ω. In this paper, we will prove various statistical properties of Z …