1 citations · 2 across the 6 of their papers we have counts for
7 papers
Gaussian Convolution, Internal Energies, and the Kneser--Poulsen Conjecture
Gautam Aishwarya, Dongbin Li
We study to what extent the majorisation order between a probability measure and its -Lipschitz image is preserved when both measures undergo Gaussian convolution. We show that…
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 tensor is matrix displacement convex. As an application, under the assumpt…
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…
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…
Stability in the Banach isometric conjecture and nearly monochromatic Finsler surfaces
Gautam Aishwarya, Dmitry Faifman
The Banach isometric conjecture asserts that a normed space with all of its -dimensional subspaces isometric, where , is Euclidean. The first case of is classical…
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 transport…