Galton-Watson Process

The Galton-Watson process is a mathematical model used to describe how populations evolve over generations, where each individual produces a random number of offspring based on a fixed probability distribution. Starting with a certain number of individuals, the process tracks how the population changes over time, considering that some lineages may die out while others grow. It helps understand phenomena like species extinction or proliferation, and is fundamental in fields such as genetics, ecology, and probability theory for analyzing random branching behaviors.