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PreprintCC BY 4.0arXiv

Moment estimates for chaoses with regular moment growth

  • Rafał Meller
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Abstract

We give two-sided moment estimates for decoupled chaoses of any order generated by independent symmetric random variables with regular moment growth: |X|2p≤ K|X|p for every p≥1. The estimates involve only the coefficient tensor and the one-dimensional tails. They use the partition norms of Adamczak and Latała, with constants depending only on the order and on K. The proof starts with log-concave tails. Gaussian smoothing gives the estimate for the expected norm needed for induction, and a product comparison reduces the remaining distributions to this case. The extra tensor indices introduced by the comparison are removed using Rademacher moments. A comparison with products of log-concave-tail variables then extends the formula to regular moment growth. We also give tail bounds and explicit Rademacher and Weibull formulas for r≥1, including fourth-order examples. This article was developed with the assistance of GPT Astra-6.

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Cite

BibTeXRIS
BibTeX
@misc{meller2026moment,
  title = {{Moment estimates for chaoses with regular moment growth}},
  author = {Rafał Meller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05829},
  eprint = {2610.05829},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05829},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Moment estimates for chaoses with regular moment growth
AU  - Rafał Meller
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05829
UR  - https://arxiv.org/abs/2610.05829
AB  - We give two-sided moment estimates for decoupled chaoses of any order generated by independent symmetric random variables with regular moment growth: |X|_2p≤ K|X|_p for every p≥1. The estimates involve only the coefficient tensor and the one-dimensional tails. They use the partition norms of Adamczak and Latała, with constants depending only on the order and on K. The proof starts with log-concave tails. Gaussian smoothing gives the estimate for the expected norm needed for induction, and a product comparison reduces the remaining distributions to this case. The extra tensor indices introduced by the comparison are removed using Rademacher moments. A comparison with products of log-concave-tail variables then extends the formula to regular moment growth. We also give tail bounds and explicit Rademacher and Weibull formulas for r≥1, including fourth-order examples. This article was developed with the assistance of GPT Astra-6.
ER  -