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PreprintarXiv licencearXiv

Stability of the Courtade-Kumar inequality

  • Vu Khac Ky
  • Tuan Tran
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Abstract

We prove dimension-independent stability for the Courtade-Kumar inequality: a Boolean function f:{−1,1}n→{−1,1} whose information is close to the dictator value is close in probability to a signed dictator. The correlation dependence is sharp in order near zero and, for increasing functions, also at the noiseless endpoint.

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Cite

BibTeXRIS
BibTeX
@misc{ky2026stability,
  title = {{Stability of the Courtade-Kumar inequality}},
  author = {Vu Khac Ky and Tuan Tran},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31797},
  eprint = {2609.31797},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31797},
}
RIS
TY  - UNPB
TI  - Stability of the Courtade-Kumar inequality
AU  - Vu Khac Ky
AU  - Tuan Tran
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31797
UR  - https://arxiv.org/abs/2609.31797
AB  - We prove dimension-independent stability for the Courtade-Kumar inequality: a Boolean function f:{−1,1}^n→{−1,1} whose information is close to the dictator value is close in probability to a signed dictator. The correlation dependence is sharp in order near zero and, for increasing functions, also at the noiseless endpoint.
ER  -