An Elementary Proof of the Inequality $χ\leq χ^*$ for Conditional Free Entropy
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909156367138816 |
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| author | Jekel, David Pi, Jennifer |
| author_facet | Jekel, David Pi, Jennifer |
| contents | Through the study of large deviations theory for matrix Brownian motion, Biane-Capitaine-Guionnet proved the inequality $χ(X) \leq χ^*(X)$ that relates two analogs of entropy in free probability defined by Voiculescu. We give a new proof of $χ\leq χ^*$ that is elementary in the sense that it does not rely on stochastic differential equations and large deviation theory. Moreover, we generalize the result to conditional microstates and non-microstates free entropy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_02574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Elementary Proof of the Inequality $χ\leq χ^*$ for Conditional Free Entropy Jekel, David Pi, Jennifer Operator Algebras Probability 46L53, 46L54, 60B20, 94A17 Through the study of large deviations theory for matrix Brownian motion, Biane-Capitaine-Guionnet proved the inequality $χ(X) \leq χ^*(X)$ that relates two analogs of entropy in free probability defined by Voiculescu. We give a new proof of $χ\leq χ^*$ that is elementary in the sense that it does not rely on stochastic differential equations and large deviation theory. Moreover, we generalize the result to conditional microstates and non-microstates free entropy. |
| title | An Elementary Proof of the Inequality $χ\leq χ^*$ for Conditional Free Entropy |
| topic | Operator Algebras Probability 46L53, 46L54, 60B20, 94A17 |
| url | https://arxiv.org/abs/2305.02574 |