Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 45 min ago
PreprintCC BY-NC-SA 4.0arXiv

An O(1) Bound for the KLS Constant

  • Zhao Song
  • Xinzhi Zhang
Open at sourcePDFDOICite

Abstract

The Kannan--Lovász--Simonovits (KLS) conjecture asks whether every isotropic log-concave probability measure on ℝn has a Cheeger constant bounded below by a universal positive constant. We prove that ψn≤ C for a universal constant C>0, resolving the KLS conjecture. We also prove that CP(μ)≤ C' for every isotropic log-concave probability measure μ on ℝn, with a universal constant C'>0.

Related

  1. Information Lower Bound for Regime Boundary Estimation — Optimal Precision Limit at the n² Scale and Universal Constant c=1/8 in the Fixed-Breakpoint Model
    Shuiping Tang
    Zenodo (CERN European Organization for Nuclear Research)PreprintLicence not stated7 citedStatisticsOpenAlex
  2. An Improved Lower Bound for the Complex Grothendieck Constant
    Shengtao Guo, Ethan X. Fang, Junwei Lu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. A computer-assisted upper bound of 1.7813 for the real Grothendieck constant
    Bo Peng
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. An exact hierarchy for Lebesgue's universal covering constant and a certified 0.834 lower bound
    Shuai Zeng
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. A Model-threshold Dimension Bound and Sharp Critical Ends for Smooth Singular Sets of Constant Positive σk-curvature Metrics
    Jiahuan Li, Yilu Liu, Xi-Nan Ma
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{song2026bound,
  title = {{An $O(1)$ Bound for the KLS Constant}},
  author = {Zhao Song and Xinzhi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01447},
  eprint = {2610.01447},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01447},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - An O(1) Bound for the KLS Constant
AU  - Zhao Song
AU  - Xinzhi Zhang
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.01447
UR  - https://arxiv.org/abs/2610.01447
AB  - The Kannan--Lovász--Simonovits (KLS) conjecture asks whether every isotropic log-concave probability measure on ℝ^n has a Cheeger constant bounded below by a universal positive constant. We prove that ψ_n≤ C for a universal constant C>0, resolving the KLS conjecture. We also prove that C_P(μ)≤ C' for every isotropic log-concave probability measure μ on ℝ^n, with a universal constant C'>0.
ER  -