A Generalized Central Limit Conjecture for Convex Bodies

Explore a 46-minute theory seminar lecture on "A Generalized Central Limit Conjecture for Convex Bodies" presented by Haotian Jiang from the University of Washington. Delve into the proposed generalized Central Limit Theorem (CLT) for marginals along random directions drawn from isotropic log-concave distributions. Examine the main result demonstrating the quantitative equivalence between this generalized CLT and the KLS conjecture. Investigate how polynomial improvements in the current KLS bound of n^(1/4) in R^n relate to the generalized CLT, and vice versa. Consider the potential insights this tight connection might provide into open questions in asymptotic convex geometry. Recorded on October 29, 2019, this closed-captioned lecture is part of the Paul G. Allen School's theory seminar series.