2024/11/14 by Airam Blancas, Blancas, Airam, María Clara Fittipaldi +3
Computer Science · Mathematics · Physics and Astronomy · #60J80 #60K35 #82B43 #92D25 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2411.09621
openalex publication_date 2024/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this survey, we explore the connections between two areas of probability: percolation theory and population genetic models. Our first goal is to highlight a construction on Galton-Watson trees, which has been described in two different ways: Bernoulli bond percolation and neutral mutations. Next, we introduce a novel connection between the Divide-and-Color percolation model and a particular multi-type Galton-Watson tree. We provide a gentle introduction to these topics while presenting an overview of the results that connect them.