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An efficiency upper bound for inverse covariance estimation
Ronen Eldan
We derive an upper bound for the efficiency of estimating entries in the inverse covariance matrix of a high dimensional distribution. We show that in order to approximate an off-d…
Dimensionality and the stability of the Brunn-Minkowski inequality
Ronen Eldan, Bo`az Klartag
We prove stability estimates for the Brunn-Minkowski inequality for convex sets. Unlike existing stability results, our estimates improve as the dimension grows. Our results are eq…
Convex Hulls in the Hyperbolic Space
Itai Benjamini, Ronen Eldan
We show that there exists a universal constant C>0 such that the convex hull of any N points in the hyperbolic space H^n is of volume smaller than C N, and that for any dimension n…
Extremal points of high dimensional random walks and mixing times of a Brownian motion on the sphere
Ronen Eldan
We derive asymptotics for the probability of the origin to be an extremal point of a random walk in R^n. We show that in order for the probability to be roughly 1/2, the number of…