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In this chapter, we explore the connections between two areas of probability: percolation theory and population genetic models. Our first goal is to highlight a construction on Bienaymé-Galton-Watson trees, which has been described in two different ways: as Bernoulli bond percolation and as neutral mutations. Next, we introduce a novel connection between the Divide-and-Color percolation model and a particular multi-type Bienaymé-Galton-Watson tree. We provide a gentle introduction to these topics while presenting an overview of the results that connect them.

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Crossing Bridges Between Percolation Models and Bienaymé-Galton-Watson Trees

  • 会议论文

  • 发表日期：

    2025年

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  • Airam Blancas,
  • María Clara Fittipaldi,
  • Saraí Hernández-Torres

摘要

In this chapter, we explore the connections between two areas of probability: percolation theory and population genetic models. Our first goal is to highlight a construction on Bienaymé-Galton-Watson trees, which has been described in two different ways: as Bernoulli bond percolation and as neutral mutations. Next, we introduce a novel connection between the Divide-and-Color percolation model and a particular multi-type Bienaymé-Galton-Watson tree. We provide a gentle introduction to these topics while presenting an overview of the results that connect them.