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PreprintarXiv licencearXiv

The skeleton-blocks decomposition of Bienaymé trees, and applications to their local convergence

  • Marc Bernard
  • Robin Stephenson
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Abstract

We study multi-type critical Bienaymé trees through the lens of the skeleton-blocks structure, seeing them as a monotype skeleton on which we have added multi-type blocks. This decomposition enjoys a remarkably elegant compatibility with the concept of local convergence, allowing us to find simple proofs of traditional local limit theorems.

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Cite

BibTeXRIS
BibTeX
@misc{bernard2026skeletonblocks,
  title = {{The skeleton-blocks decomposition of Bienaymé trees, and applications to their local convergence}},
  author = {Marc Bernard and Robin Stephenson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20657},
  eprint = {2609.20657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20657},
}
RIS
TY  - UNPB
TI  - The skeleton-blocks decomposition of Bienaymé trees, and applications to their local convergence
AU  - Marc Bernard
AU  - Robin Stephenson
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20657
UR  - https://arxiv.org/abs/2609.20657
AB  - We study multi-type critical Bienaymé trees through the lens of the skeleton-blocks structure, seeing them as a monotype skeleton on which we have added multi-type blocks. This decomposition enjoys a remarkably elegant compatibility with the concept of local convergence, allowing us to find simple proofs of traditional local limit theorems.
ER  -