Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00451 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913714106531840 |
|---|---|
| author | Langharst, Dylan |
| author_facet | Langharst, Dylan |
| contents | In a series of works, Lutwak, Yang and Zhang established what could be called affine information theory, which is the study of moment-entropy and Fisher-information-type inequalities that are invariant with respect to affine transformations for random vectors. Their set of tools stemmed from sharp affine isoperimetric inequalities in the $L^p$ Brunn-Minkowski theory of convex geometry they had established. In this work, we generalize the affine information theory to the setting of matrices. These inequalities on the space of $n\times m$ matrices are induced by the interaction between $\mathbb{R}^n$ with its Euclidean structure and $\mathbb{R}^m$ equipped with a pseudo-norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Moment-Entropy inequalities in the space of matrices Langharst, Dylan Functional Analysis Probability 52A20, 52A40, Secondary: 94A17, 94A17 In a series of works, Lutwak, Yang and Zhang established what could be called affine information theory, which is the study of moment-entropy and Fisher-information-type inequalities that are invariant with respect to affine transformations for random vectors. Their set of tools stemmed from sharp affine isoperimetric inequalities in the $L^p$ Brunn-Minkowski theory of convex geometry they had established. In this work, we generalize the affine information theory to the setting of matrices. These inequalities on the space of $n\times m$ matrices are induced by the interaction between $\mathbb{R}^n$ with its Euclidean structure and $\mathbb{R}^m$ equipped with a pseudo-norm. |
| title | On Moment-Entropy inequalities in the space of matrices |
| topic | Functional Analysis Probability 52A20, 52A40, Secondary: 94A17, 94A17 |
| url | https://arxiv.org/abs/2503.00451 |