Functional inequalities for Boolean entropy
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910034783371264 |
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| author | Cébron, Guillaume Pan, Kewei |
| author_facet | Cébron, Guillaume Pan, Kewei |
| contents | Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fisher information in the Boolean Central Limit Theorem and establish several functional inequalities involving these quantities, including a logarithmic Sobolev inequality. We also develop Non-microstate counterparts and prove the associated functional inequalities. In addition, we introduce a notion of Stein discrepancy in the Boolean setting, which leads to new Berry--Esseen type bounds in the Boolean central limit theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23527 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Functional inequalities for Boolean entropy Cébron, Guillaume Pan, Kewei Probability Information Theory Operator Algebras Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fisher information in the Boolean Central Limit Theorem and establish several functional inequalities involving these quantities, including a logarithmic Sobolev inequality. We also develop Non-microstate counterparts and prove the associated functional inequalities. In addition, we introduce a notion of Stein discrepancy in the Boolean setting, which leads to new Berry--Esseen type bounds in the Boolean central limit theorem. |
| title | Functional inequalities for Boolean entropy |
| topic | Probability Information Theory Operator Algebras |
| url | https://arxiv.org/abs/2602.23527 |