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Theorem · version 1

Transporting the proposed bound beyond isotropic measures

Statement

If every isotropic log-concave probability measure has Poincaré constant at most C, then every full-dimensional log-concave probability measure μ with covariance Σ satisfies C_P(μ) ≤ C ‖Σ‖op.

Assumptions

  • Finite nonsingular covariance and a log-concave probability density.
  • The same universal constant C is assumed in the isotropic theorem.

Scope

This affine-transfer implication does not establish the premise or a numerical value of C. Singular covariance requires a formulation on its affine support.

Evidence

Connections

Sources

Presenting a proof of the Kannan–Lovász–Simonovits conjecture →

  • Theorem 1.1 and proof/AI acknowledgement → · Original passage ↗
    Recorded wording

    Proposes a dimension-free Poincaré bound for isotropic log-concave measures through cumulant estimates, localization and suspension.

    paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Pierre Bizeul · Boaz Klartag · Joseph Lehec · Preprint · Publication date Oct 4, 2026

Revision & attribution

Source revision: 2026-10-04. Observed Oct 13, 2026.

The authors credit ChatGPT with many proof ideas and arguments, and credit the suspension idea and exposition to the human authors. Their approach uses a criterion of Song and Zhang; these are distinct papers with a mathematical dependency, not wholly independent proofs.

History

Statement versions

Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.

Assessment history · 1

Assessments retained in these publication records. Earlier statement versions retain their own source histories.

Record details
Claim ID
claim-kls-conjecture-consequence
Statement version
1
SHA-256
d0aec6e422cdec5a9a802054ea79ff9382159323b74a2e929b345022586ea068

Publication records