Concentration of norms of random vectors with independent $p$-sub-exponential coordinates
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866918248433319936 |
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| author | Zajkowski, Krzysztof |
| author_facet | Zajkowski, Krzysztof |
| contents | We present examples of $p$-sub-exponential random variables for any positive $p$. We prove two types of concentration of standard $p$-norms ($2$-norm is the Euclidean norm) of random vectors with independent $p$-sub-exponential coordinates around the Lebesgue $L^p$-norms of these $p$-norms of random vectors. In the first case $p\ge 1$, our estimates depend on the dimension $n$ of random vectors. But in the second one for $p\ge 2$, with an additional assumption, we get an estimate that does not depend on $n$. In other words, we generalize some know concentration results in the Euclidean case to cases of the $p$-norms of random vectors with independent $p$-sub-exponential coordinates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_06776 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Concentration of norms of random vectors with independent $p$-sub-exponential coordinates Zajkowski, Krzysztof Probability 60E15, 46E30 We present examples of $p$-sub-exponential random variables for any positive $p$. We prove two types of concentration of standard $p$-norms ($2$-norm is the Euclidean norm) of random vectors with independent $p$-sub-exponential coordinates around the Lebesgue $L^p$-norms of these $p$-norms of random vectors. In the first case $p\ge 1$, our estimates depend on the dimension $n$ of random vectors. But in the second one for $p\ge 2$, with an additional assumption, we get an estimate that does not depend on $n$. In other words, we generalize some know concentration results in the Euclidean case to cases of the $p$-norms of random vectors with independent $p$-sub-exponential coordinates. |
| title | Concentration of norms of random vectors with independent $p$-sub-exponential coordinates |
| topic | Probability 60E15, 46E30 |
| url | https://arxiv.org/abs/1909.06776 |