PreprintCC BY 4.0arXiv
Mean-field branching SDEs: propagation of chaos, scaling limits and phase transitions
Abstract
We study branching SDEs with law-dependent immigration and their mean-field particle approximations. Under a dissipativity condition and sufficiently weak interaction, a uniform propagation-of-chaos bound in time of order N−1/2 is established. On every fixed finite time horizon, the same order of propagation of chaos holds for arbitrary finite interaction strength. A two-stage scaling limit connects continuous-time discrete-state mean-field birth--death processes to interacting branching diffusions and then to the nonlinear equation. For a logistic mean-field diffusion we prove a sharp criterion for extinction/non-extinction, and further show that weak enough interaction strength is necessary for a uniform-in-time approximation.
Related
- Scaling limits of critical branching random walks and their snakes
- Principal eigenvalues of nonlocal operators with advection: sharp scaling limits and spectral phase transitions
- Fluctuations of additive martingale limits of branching Brownian motion
- Serrin-type overdetermination in scaling limits: Sharp existence and asymptotic behavior of quasi-linear Schrödinger energy ground states
- Homological branching laws for p-adic and mod p representations of GL2 over a p-adic field
BibTeX
@misc{chen2026meanfield,
title = {{Mean-field branching SDEs: propagation of chaos, scaling limits and phase transitions}},
author = {Shukai Chen and Lina Ji and Xiaowen Zhou},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29797},
eprint = {2608.29797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29797},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mean-field branching SDEs: propagation of chaos, scaling limits and phase transitions
AU - Shukai Chen
AU - Lina Ji
AU - Xiaowen Zhou
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29797
UR - https://arxiv.org/abs/2608.29797
AB - We study branching SDEs with law-dependent immigration and their mean-field particle approximations. Under a dissipativity condition and sufficiently weak interaction, a uniform propagation-of-chaos bound in time of order N^−1/2 is established. On every fixed finite time horizon, the same order of propagation of chaos holds for arbitrary finite interaction strength. A two-stage scaling limit connects continuous-time discrete-state mean-field birth--death processes to interacting branching diffusions and then to the nonlinear equation. For a logistic mean-field diffusion we prove a sharp criterion for extinction/non-extinction, and further show that weak enough interaction strength is necessary for a uniform-in-time approximation.
ER -