10 papers
Thin-Shell implies small-ball deviation via Gaussian tilts
Silouanos Brazitikos, Emanuel Milman
We show that uniform thin-shell estimates for (even) isotropic log-concave measures on yield precise and explicit deviation estimates for the Euclidean norm $|X|…
Operationalizing Cyber Threat Intelligence with GraphRAG
Atul Kabra, Prakhar Paliwal, Manjesh K. Hanawal
When a security researcher publishes a report on a cyberattack, detection engineers are supposed to turn it into working detection rules. In practice, most automated attempts at th…
The Gaussian Conjugate Rogers-Shephard Inequality
Emanuel Milman, Shohei Nakamura, Hiroshi Tsuji
We fuse between the Rogers-Shephard inequality for the Lebesgue measure and Royen's Gaussian Correlation Inequality, simultaneously extending both into a single sharp inequality fo…
On the connectedness of a minimizing cluster's boundary
Emanuel Milman, Joe Neeman
We verify that an isoperimetric minimizing cluster on a simply connected homogeneous Riemannian manifold with at most one end always has connected boundary. In particular, the boun…
Gaussian Correlation via Inverse Brascamp-Lieb
Emanuel Milman
We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequali…
Isoperimetric Inequalities on Slabs with applications to Cubes and Gaussian Slabs
Emanuel Milman
We study isoperimetric inequalities on "slabs", namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension-o…