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The site frequency spectrum for coalescing Brownian motion

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  • Shuai, Yubo

Abstract

Motivated by the goal of understanding the genealogy of a sample from an expanding population in the plane, we consider coalescing Brownian motion on the circle. For this model, we establish a weak law of large numbers for the site frequency spectrum. A parallel result holds for a localized version where the genealogy is modeled by coalescing Brownian motion on the line.

Suggested Citation

  • Shuai, Yubo, 2025. "The site frequency spectrum for coalescing Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:spapps:v:180:y:2025:i:c:s0304414924002291
    DOI: 10.1016/j.spa.2024.104521
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    References listed on IDEAS

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    1. Blath, Jochen & Cronjäger, Mathias Christensen & Eldon, Bjarki & Hammer, Matthias, 2016. "The site-frequency spectrum associated with Ξ-coalescents," Theoretical Population Biology, Elsevier, vol. 110(C), pages 36-50.
    2. Gunnarsson, Einar Bjarki & Leder, Kevin & Foo, Jasmine, 2021. "Exact site frequency spectra of neutrally evolving tumors: A transition between power laws reveals a signature of cell viability," Theoretical Population Biology, Elsevier, vol. 142(C), pages 67-90.
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