English

The slicing conjecture via small ball estimates

Functional Analysis 2025-01-14 v1 Probability

Abstract

Bourgain's slicing conjecture was recently resolved by Joseph Lehec and Bo'az Klartag. We present an alternative proof by establishing small ball probability estimates for isotropic log-concave measures. Our approach relies on the stochastic localization process and Guan's bound, techniques also used by Klartag and Lehec. The link between small ball probabilities and the slicing conjecture was first observed by Dafnis and Paouris and is established through Milman's theory of M-ellipsoids.

Cite

@article{arxiv.2501.06854,
  title  = {The slicing conjecture via small ball estimates},
  author = {Pierre Bizeul},
  journal= {arXiv preprint arXiv:2501.06854},
  year   = {2025}
}

Comments

12 pages

R2 v1 2026-06-28T21:03:57.470Z