Branching Process (Galton-Watson Process)

Here are some simulations of branching trees and the Galton-Watson Process
(click on a picture to get a bigger version of it):

     
     


Here is some additional reading on random walks:

• A book Probability on Trees and Networks by Russell Lyons with Yuval Peres. Chapters 4 and 10 are of particular interest.
  
  
• A nice recent paper by Peter E. Ney and Anand N. Vidyashankar on the growth of supercritical branching processes.
  
  
• A short proof of the Kesten-Stigum theorem by Russell Lyons, Robin Pemantle, and Yuval Peres.
  
  
• A paper by Robin Pemantle, Yuval Peres comparing Galton-Watson trees with deterministic trees.