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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1812.01845 |
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| _version_ | 1866911132304801792 |
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| author | Chakraborty, Somnath Narayanan, Hariharan |
| author_facet | Chakraborty, Somnath Narayanan, Hariharan |
| contents | We develop a randomized algorithm (that succeeds with high probability) for generating an $ε$-net in a sphere of dimension n. The basic scheme is to pick $O(n \ln(1/n) + \ln(1/δ))$ random rotations and take all possible words of length $O(n \ln(1/ε))$ in the same alphabet and act them on a fixed point. We show this set of points is equidistributed at a scale of $ε$. Our main application is to approximate integration of Lipschitz functions over an n-sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_01845 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Generating an equidistributed net on a unit n-sphere using random rotations Chakraborty, Somnath Narayanan, Hariharan Probability Computational Geometry We develop a randomized algorithm (that succeeds with high probability) for generating an $ε$-net in a sphere of dimension n. The basic scheme is to pick $O(n \ln(1/n) + \ln(1/δ))$ random rotations and take all possible words of length $O(n \ln(1/ε))$ in the same alphabet and act them on a fixed point. We show this set of points is equidistributed at a scale of $ε$. Our main application is to approximate integration of Lipschitz functions over an n-sphere. |
| title | Generating an equidistributed net on a unit n-sphere using random rotations |
| topic | Probability Computational Geometry |
| url | https://arxiv.org/abs/1812.01845 |