5 papers
Metric complexity is a Bryant--Tupper diversity
Gautam Aishwarya, Dongbin Li, Mokshay Madiman +1
The metric complexity (sometimes called Leinster--Cobbold maximum diversity) of a compact metric space is a recently introduced isometry-invariant of compact metric spaces which ge…
Entropic and functional forms of the dimensional Brunn--Minkowski inequality in Gauss space
Gautam Aishwarya, Dongbin Li
Given even strongly log-concave random vectors and in , we show that a natural joint distribution satisfies, \begin{equation} e^{ - \f…
New Brunn--Minkowski and functional inequalities via convexity of entropy
Gautam Aishwarya, Liran Rotem
We study the connection between the concavity properties of a measure and the convexity properties of the associated relative entropy along optimal transpo…
Sectional curvature and matrix displacement convexity
Gautam Aishwarya, Liran Rotem, Yair Shenfeld
We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy functional is matrix displacement convex. As an application we obtain intr…
The Kneser--Poulsen phenomena for entropy
Gautam Aishwarya, Dongbin Li
The Kneser--Poulsen conjecture asserts that the volume of a union of balls in Euclidean space cannot be increased by bringing their centres pairwise closer. We prove that its natur…