From Cannings model to Brownian motion conditioned on local time profile
Probability
2026-02-04 v2
Abstract
We study the scaling limits of genealogical trees arising from Cannings models. Under suitable moment conditions, we show that the rescaled contour and height functions converge to a time change of Brownian motion conditioned on a given local time profile. This conditioned Brownian motion is a self-interacting diffusion constructed independently by Warren--Yor (1998) and Aldous (1998). A key ingredient in our proof is a sequential version of the coming-down-from-infinity property.
Keywords
Cite
@article{arxiv.2511.09517,
title = {From Cannings model to Brownian motion conditioned on local time profile},
author = {Xiaodan Li and Chengshi Wang and Yushu Zheng},
journal= {arXiv preprint arXiv:2511.09517},
year = {2026}
}
Comments
50 pages, 3 figures