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Central Limit Theorems for Finitary Factors of iid Processes

  • Raimundo Briceño
  • Zemer Kosloff
  • Nicolò Paviato
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Abstract

We study statistical limit theorems for time-series generated by multidimensional random fields that are finitary factors of iid random processes. Based on the decay of the tail of the coding radius, we establish the Central Limit Theorem with explicit rates of convergence, as well as the weak convergence to a Brownian sheet, for suitably regular functions. Our results can be applied to a variety of classical models in statistical mechanics, such as the Ising model, the hard-core model, and proper colourings.

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Cite

BibTeXRIS
BibTeX
@misc{briceno2026central,
  title = {{Central Limit Theorems for Finitary Factors of iid Processes}},
  author = {Raimundo Briceño and Zemer Kosloff and Nicolò Paviato},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35332},
  eprint = {2609.35332},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35332},
}
RIS
TY  - UNPB
TI  - Central Limit Theorems for Finitary Factors of iid Processes
AU  - Raimundo Briceño
AU  - Zemer Kosloff
AU  - Nicolò Paviato
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35332
UR  - https://arxiv.org/abs/2609.35332
AB  - We study statistical limit theorems for time-series generated by multidimensional random fields that are finitary factors of iid random processes. Based on the decay of the tail of the coding radius, we establish the Central Limit Theorem with explicit rates of convergence, as well as the weak convergence to a Brownian sheet, for suitably regular functions. Our results can be applied to a variety of classical models in statistical mechanics, such as the Ising model, the hard-core model, and proper colourings.
ER  -