A central limit theorem for convex sets

@sp_monte_carlo @_lebellig True not just of sphere but of convex set in general -- mass gets concentrated in a zero-width slice https://t.co/ggtX7Juio0

@srchvrs @thomasahle Projection isn't hedgehog, however, cube behaves like a hedgehog as the distance between sphere inscribed into cube corner and the corner point goes to infinity with d. There's also this https://t.co/ggtX7Juio0, another way of formaliz

@james_r_lucas @david_madras @CasualBrady @ethancaballero Alternatively, when looking at slices perpendicular to a vector, for almost all vectors there will be one big slice, and the rest are negligible -- https://t.co/ggtX7JtKys

"We argue that convexity - and perhaps geometry in general - may replace the role of independence in certain aspects of the phenomenon represented by the central limit theorem." (from https://t.co/HbQyAdElhR)

@ovrdr If the diameter is 1, area graph is approximately Gaussian, scaled by 1/sqrt(n). This also means that in high dimensions, an arbitrary convex shape will have almost all of its mass concentrated in the middle slice https://t.co/ggtX7Jc99S

RT @pdenapo: Supongamos que tenemos un vector aleatorio que se distribuye al azar en un convexo de dimensión grande. Entonces sus proyeccio…