TL;DR
This paper explores stability estimates related to the logarithmic Sobolev inequality, establishing new $W^{1,1}$ bounds in one dimension and examining $W_1$-quantitative estimates linked to uncertainty principles.
Contribution
It introduces novel $W^{1,1}$ stability estimates for the logarithmic Sobolev inequality in one dimension and investigates related $W_1$-quantitative bounds.
Findings
Established $W^{1,1}$ stability bounds in one dimension.
Derived $W_1$-quantitative estimates connected to uncertainty principles.
Linked stability estimates to fundamental inequalities in mathematical physics.
Abstract
The logarithmic Sobolev inequality is fundamental in mathematical physics. Associated stability estimates are equivalent to uncertainty principles. Via a second moment bound, estimates are obtained in one dimension and similar -quantitative estimates are investigated.
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
TopicsStability and Controllability of Differential Equations · Stability and Control of Uncertain Systems · Numerical methods for differential equations