Convergence of weighted branching processes
Probability
2025-12-09 v1
Abstract
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and non-geometric rescaling. We demonstrate applications to Galton-Watson trees indexed by random weights and by random kernels, convergence in Wasserstein distance of the underlying mean semi-group, and convergence of ergodic averages along lineages.
Cite
@article{arxiv.2512.07653,
title = {Convergence of weighted branching processes},
author = {Denis Villemonais and Nicolas Zalduendo},
journal= {arXiv preprint arXiv:2512.07653},
year = {2025}
}
Comments
26 pages