Invariance principles for tree-valued Cannings chains
Abstract
We consider sequences of tree-valued Markov chains that describe evolving genealogies in Cannings models, and we show their convergence in distribution to tree-valued Fleming-Viot processes. Under the conditions of M\"ohle and Sagitov, this convergence holds for all tree-valued Fleming-Viot processes under consideration in the dust-free case, and for the Fleming-Viot processes with values in the space of distance matrix distributions in the case with dust. Convergence to Fleming-Viot processes with values in the space of marked metric measure spaces in the case with dust is ensured by an additional assumption on the probability that a randomly sampled individual belongs to a non-singleton family.
Keywords
Cite
@article{arxiv.1608.08203,
title = {Invariance principles for tree-valued Cannings chains},
author = {Stephan Gufler},
journal= {arXiv preprint arXiv:1608.08203},
year = {2017}
}
Comments
31 pages. Proposition 7.3 in this paper is split off from arXiv:1404.3682v2. In v2 of the present paper, the title is changed, an index of notation is added, and there are some very minor corrections and modifications