The Localization Method for High-Dimensional Inequalities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912980628668416 |
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| author | Kook, Yunbum Vempala, Santosh S. |
| author_facet | Kook, Yunbum Vempala, Santosh S. |
| contents | We survey the localization method for proving inequalities in high dimension, pioneered by Lovász and Simonovits (1993), and its stochastic extension developed by Eldan (2012). The method has found applications in a surprising wide variety of settings, ranging from its original motivation in isoperimetric inequalities to optimization, concentration of measure, and bounding the mixing rate of Markov chains. At heart, the method converts a given instance of an inequality (for a set or distribution in high dimension) into a highly structured instance, often just one-dimensional. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10848 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Localization Method for High-Dimensional Inequalities Kook, Yunbum Vempala, Santosh S. Probability Data Structures and Algorithms Functional Analysis We survey the localization method for proving inequalities in high dimension, pioneered by Lovász and Simonovits (1993), and its stochastic extension developed by Eldan (2012). The method has found applications in a surprising wide variety of settings, ranging from its original motivation in isoperimetric inequalities to optimization, concentration of measure, and bounding the mixing rate of Markov chains. At heart, the method converts a given instance of an inequality (for a set or distribution in high dimension) into a highly structured instance, often just one-dimensional. |
| title | The Localization Method for High-Dimensional Inequalities |
| topic | Probability Data Structures and Algorithms Functional Analysis |
| url | https://arxiv.org/abs/2512.10848 |