Stable limits for the clone-mutant chain with mother-dependent mutation

@misc{blancas2026stable,
  title = {{Stable limits for the clone-mutant chain with mother-dependent mutation}},
  author = {Airam Blancas and María Clara Fittipaldi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37815},
  eprint = {2610.37815},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37815},
}

TY  - UNPB
TI  - Stable limits for the clone-mutant chain with mother-dependent mutation
AU  - Airam Blancas
AU  - María Clara Fittipaldi
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37815
UR  - https://arxiv.org/abs/2610.37815
AB  - We consider the general mother-dependent neutral mutation model defined in Blancas, Fittipaldi and Hernández-Torres (2026), consisting of a multitype branching process in which every individual carries one of d alleles and each mutant child acquires a type different from that of its mother, according to a prescribed distribution. We assume that the total offspring distribution is critical and belongs to the domain of attraction of an α-stable law, with α∈(1,2), while mutations are rare. Extending the results of Blancas and Rivero (2018), we prove the finite-dimensional convergence of the rescaled Markov chain that records, in each allelic generation, the sizes of the type-specific clone subfamilies and the mutant populations they produce. The limiting clone masses form a multitype Jiřina process driven by stable subordinators with drift, whose branching mechanism combines the stable reproduction law with the mother-dependent mutation matrix.
ER  -