Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Kook, Yunbum, Vempala, Santosh S.
Institution: Georgia Institute of Technology
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4417296905
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