Isoperimetric problem for exponential measure on the plane with l_1-metric
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arXiv
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| Format: | Preprint |
| Publié: |
2016
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| _version_ | 1866909474779824128 |
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| author | Strzelecka, Marta |
| author_facet | Strzelecka, Marta |
| contents | We give a solution to the isoperimetric problem for the exponential measure on the plane with the $\ell_1$-metric. As it turns out, among all sets of a given measure, the simplex or its complement (i.e. the ball in the $\ell_1$-metric or its complement) has the smallest boundary measure. The proof is based on a symmetrisation (along the sections of equal $\ell_1$-distance from the origin). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1606_03342 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Isoperimetric problem for exponential measure on the plane with l_1-metric Strzelecka, Marta Probability 52A40, 60E15 We give a solution to the isoperimetric problem for the exponential measure on the plane with the $\ell_1$-metric. As it turns out, among all sets of a given measure, the simplex or its complement (i.e. the ball in the $\ell_1$-metric or its complement) has the smallest boundary measure. The proof is based on a symmetrisation (along the sections of equal $\ell_1$-distance from the origin). |
| title | Isoperimetric problem for exponential measure on the plane with l_1-metric |
| topic | Probability 52A40, 60E15 |
| url | https://arxiv.org/abs/1606.03342 |