Exponential and Gaussian concentration of 1-Lipschitz maps
Kei Funano
TL;DR
This paper establishes exponential and Gaussian concentration inequalities for 1-Lipschitz maps from mm-spaces to Hadamard manifolds, addressing a question posed by Gromov.
Contribution
It provides a complete answer to Gromov's question by proving new concentration inequalities for Lipschitz maps into Hadamard manifolds.
Findings
Proves exponential concentration inequality for 1-Lipschitz maps.
Establishes Gaussian concentration inequality for 1-Lipschitz maps.
Addresses a longstanding open question by Gromov.
Abstract
In this paper, we prove an exponential and Ganssian concentration inequality for 1-Lipschitz maps from mm-spaces to Hadamard manifolds. In particular, we give a complete answer to a question by M. Gromov.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Nonlinear Partial Differential Equations