The Kannan-Lov'asz-Simonovits Conjecture
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Abstract (arXiv)
The Kannan-Lov'asz-Simonovits conjecture says that the Cheeger constant of any logconcave density is achieved to within a universal, dimension-independent constant factor by a hyperplane-induced subset. Here we survey the origin and consequences of the conjecture (in geometry, probability, information theory and algorithms) as well as recent progress resulting in the current best bounds. The conjecture has lead to several techniques of general interest.
Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jul 2018.
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Citing papers per year: 2022: 1; 2023: 2; 2024: 0; 2025: 1.
4 papers.
- 2023Tester-Learners for Halfspaces: Universal Algorithmscited by 17
- 2022Optimal Sublinear Sampling of Spanning Trees and Determinantal Point Processes via Average-Case Entropic Independencecited by 8
- 2023Spectral Clustering on Large Datasets: When Does it Work? Theory from Continuous Clustering and Density Cheeger-Busercited by 0
- 2025Improved generalization bounds for binary linear classification via isoperimetrycited by 0
- 2025Improved generalization bounds for binary linear classification via isoperimetry22 May 2025
- 2023Tester-Learners for Halfspaces: Universal Algorithms19 May 2023
- 2023Spectral Clustering on Large Datasets: When Does it Work? Theory from Continuous Clustering and Density Cheeger-Buser11 May 2023
- 2022Optimal Sublinear Sampling of Spanning Trees and Determinantal Point Processes via Average-Case Entropic Independence6 Apr 2022