4 papers
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…
The Structure of Isoperimetric Bubbles on and
Emanuel Milman, Joe Neeman
The multi-bubble isoperimetric conjecture in -dimensional Euclidean and spherical spaces from the 1990's asserts that standard bubbles uniquely minimize total perimeter among al…
Plateau Bubbles and the Quintuple Bubble Theorem on
Emanuel Milman, Joe Neeman
Sullivan's multi-bubble isoperimetric conjectures in -dimensional Euclidean and spherical spaces assert that standard bubbles uniquely minimize total perimeter among all b…
Concentration Inequalities for Sums of Markov Dependent Random Matrices
Joe Neeman, Bobby Shi, Rachel Ward
We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix…