Zeros of the Brownian Sheet
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909213907746816 |
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| author | Chen, Keming Woessner, Guillaume |
| author_facet | Chen, Keming Woessner, Guillaume |
| contents | In this work we firstly answer to a question raised by Khoshnevisan in \cite[Open Problem 4]{khoshnevisan2007slices} by proving that almost surely there is no projection of big enough rank changing the Hausdorff dimension of the zeros of the Brownian sheet. Secondly, we prove that almost surely for every projection whose rank isn't matching the aforementioned condition, the projection of the zero set is the entirety of the projective space. Key words: Brownian sheet, zeros set, Hausdorff dimension, orthogonal projection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20019 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zeros of the Brownian Sheet Chen, Keming Woessner, Guillaume Probability 60G15, 60G17, 60G60 In this work we firstly answer to a question raised by Khoshnevisan in \cite[Open Problem 4]{khoshnevisan2007slices} by proving that almost surely there is no projection of big enough rank changing the Hausdorff dimension of the zeros of the Brownian sheet. Secondly, we prove that almost surely for every projection whose rank isn't matching the aforementioned condition, the projection of the zero set is the entirety of the projective space. Key words: Brownian sheet, zeros set, Hausdorff dimension, orthogonal projection. |
| title | Zeros of the Brownian Sheet |
| topic | Probability 60G15, 60G17, 60G60 |
| url | https://arxiv.org/abs/2405.20019 |