Optimal Quantization for Nonuniform Densities on Spherical Curves
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914325665415168 |
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| author | Saha, Silpi Jha, Sangita Roychowdhury, Mrinal Kanti |
| author_facet | Saha, Silpi Jha, Sangita Roychowdhury, Mrinal Kanti |
| contents | We present an analysis of optimal quantization of probability measures with nonuniform densities on spherical curves. We begin by deriving the centroid condition, followed by a high-resolution asymptotic analysis to establish the point-density formula. We further quantify the asymptotic error formula for the nonuniform densities. We apply these theorems to the von Mises distributions and characterize the optimal condition. We also provide applications using the high-resolution asymptotic and its corresponding error formula. Our results can be used in geometric probability theory and quantization theory of spherical curves. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_11926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Quantization for Nonuniform Densities on Spherical Curves Saha, Silpi Jha, Sangita Roychowdhury, Mrinal Kanti Probability Optimization and Control 60E05, 49Q20, 53C22, 60D05, 65D30 We present an analysis of optimal quantization of probability measures with nonuniform densities on spherical curves. We begin by deriving the centroid condition, followed by a high-resolution asymptotic analysis to establish the point-density formula. We further quantify the asymptotic error formula for the nonuniform densities. We apply these theorems to the von Mises distributions and characterize the optimal condition. We also provide applications using the high-resolution asymptotic and its corresponding error formula. Our results can be used in geometric probability theory and quantization theory of spherical curves. |
| title | Optimal Quantization for Nonuniform Densities on Spherical Curves |
| topic | Probability Optimization and Control 60E05, 49Q20, 53C22, 60D05, 65D30 |
| url | https://arxiv.org/abs/2602.11926 |