Year: 2021
Type: book-chapter
Abstract: We present approximation methods that lead to law of large numbers and fluctuation results for functionals of Λ-coalescents, both in the dust-free case and in the case with a dust component. Our focus is on the tree length (or total branch length) and the total external branch length, as well as the time to the most recent common ancestor and the size of the last merger. In the second part we discuss evolving coalescents. For certain Beta-coalescents we analyse fluctuations of a class of functionals on appropriate time scales. Finally, we review results of Gufler on the representation of evolving Λ-coalescents in terms of the lookdown space.
Source: EMS series of congress reports
DOI: 10.4171/ecr/17-1/11
Authors: Götz Kersting, Anton Wakolbinger
Institution: Goethe University Frankfurt
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G500534333
OpenAlex ID: W4229814018