2 problems

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The Lovász–Vempala thin-shell variance conjecture
Let $K$ be an isotropic convex body, and let $X$ be a random point from $K$ . Lovász–Vempala variance conjecture. … Under either definition of isotropy used in the source, this conj…
Conjectureopenconvex-geometry random-walks thin-shellarXiv posted 2 days ago
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The thin-shell conjecture for isotropic logconcave measures
Thin-shell conjecture. The thin-shell constant is universally bounded:
Conjecturesolvedconvex-geometry logconcavity thin-shellarXiv posted 2 days ago

The Lovász–Vempala thin-shell variance conjecture