A Generalized Central Limit Conjecture for Convex Bodies

28 Sep 2019 Jiang Haotian Lee Yin Tat Vempala Santosh S.

The central limit theorem for convex bodies says that with high probability the marginal of an isotropic log-concave distribution along a random direction is close to a Gaussian, with the quantitative difference determined asymptotically by the Cheeger/Poincare/KLS constant. Here we propose a generalized CLT for marginals along random directions drawn from any isotropic log-concave distribution; namely, for $x,y$ drawn independently from isotropic log-concave densities $p,q$, the random variable $\langle x,y\rangle$ is close to Gaussian... (read more)

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  • FUNCTIONAL ANALYSIS
  • METRIC GEOMETRY
  • PROBABILITY