Random restrictions of high-rank tensors and polynomial maps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866913571353395200 |
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| author | Briët, Jop Castro-Silva, Davi |
| author_facet | Briët, Jop Castro-Silva, Davi |
| contents | Motivated by a problem in computational complexity, we consider the behavior of rank functions for tensors and polynomial maps under random coordinate restrictions. We show that, for a broad class of rank functions called natural rank functions, random coordinate restriction to a dense set will typically reduce the rank by at most a constant factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13728 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Random restrictions of high-rank tensors and polynomial maps Briët, Jop Castro-Silva, Davi Combinatorics Number Theory 15A69, 11B30, 68R05 Motivated by a problem in computational complexity, we consider the behavior of rank functions for tensors and polynomial maps under random coordinate restrictions. We show that, for a broad class of rank functions called natural rank functions, random coordinate restriction to a dense set will typically reduce the rank by at most a constant factor. |
| title | Random restrictions of high-rank tensors and polynomial maps |
| topic | Combinatorics Number Theory 15A69, 11B30, 68R05 |
| url | https://arxiv.org/abs/2212.13728 |