Quantum law of large numbers for Banach spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910643669434368 |
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| author | Dzhenzher, S. Sakbaev, V. |
| author_facet | Dzhenzher, S. Sakbaev, V. |
| contents | We consider random operators $Ω\to \mathcal{L}(\ell_p, \ell_p)$ for some $1 \leqslant p < \infty$. The law of large numbers is known in the case $p=2$ in the form of usual law of large numbers. Instead of sum of i.i.d. variables there may be considered the composition of random semigroups $e^{A_i t/n}$. We obtain the law of large numbers for the case $p \leqslant 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum law of large numbers for Banach spaces Dzhenzher, S. Sakbaev, V. Probability Functional Analysis We consider random operators $Ω\to \mathcal{L}(\ell_p, \ell_p)$ for some $1 \leqslant p < \infty$. The law of large numbers is known in the case $p=2$ in the form of usual law of large numbers. Instead of sum of i.i.d. variables there may be considered the composition of random semigroups $e^{A_i t/n}$. We obtain the law of large numbers for the case $p \leqslant 2$. |
| title | Quantum law of large numbers for Banach spaces |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2410.07417 |