English

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.

Keywords

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

R2 v1 2026-07-01T08:15:03.964Z