The Localization Method for High-Dimensional Inequalities
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Abstract (arXiv)
We survey the localization method for proving inequalities in high dimension, pioneered by Lov'asz 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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). First posted on arXiv 11 Dec 2025.
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Citing papers per year: 2026: 2.
2 papers.
- 2026Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Runcited by 2
- 2026On the SoS Certifiability of Log-Concave Distributionscited by 0
- 2026On the SoS Certifiability of Log-Concave Distributions24 Sep 2026
- 2026Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run17 Aug 2026