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PreprintCC BY-NC-ND 4.0arXiv

The Critical Cauchy Boundary for Gibbs Partitions

  • Fabien Baeriswyl
  • Benedikt Stufler
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Abstract

We study critical Gibbs partitions whose component law is in the domain of attraction of a spectrally positive stable law of index one. In the dense phase, we prove a local limit theorem for the number of components and functional limits for their sizes. We also describe convergent and divergent condensation regimes, and a phase transition at a boundary in which the dense and condensation contributions compete.

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Cite

BibTeXRIS
BibTeX
@misc{baeriswyl2026critical,
  title = {{The Critical Cauchy Boundary for Gibbs Partitions}},
  author = {Fabien Baeriswyl and Benedikt Stufler},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05285},
  eprint = {2611.05285},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05285},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The Critical Cauchy Boundary for Gibbs Partitions
AU  - Fabien Baeriswyl
AU  - Benedikt Stufler
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05285
UR  - https://arxiv.org/abs/2611.05285
AB  - We study critical Gibbs partitions whose component law is in the domain of attraction of a spectrally positive stable law of index one. In the dense phase, we prove a local limit theorem for the number of components and functional limits for their sizes. We also describe convergent and divergent condensation regimes, and a phase transition at a boundary in which the dense and condensation contributions compete.
ER  -