The site frequency spectrum for coalescing Brownian motion
Abstract
We consider an expanding population on the plane. The genealogy of a sample from the population is modelled by coalescing Brownian motion on the circle. We establish a weak law of large numbers for the site frequency spectrum in this model. A parallel result holds for a localized version where the genealogy is modelled by coalescing Brownian motion on the line.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2023
- DOI:
- arXiv:
- arXiv:2308.07533
- Bibcode:
- 2023arXiv230807533S
- Keywords:
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- Mathematics - Probability
- E-Print:
- 17 pages, 1 figure