3 years ago

Instability Results for the Logarithmic Sobolev Inequality and its Application to the Beckner--Hirschman Inequality.

Daesung Kim

We provide an example to show that there are no general stability results for the logarithmic Sobolev inequality in terms of the Wasserstein distances and $L^{p}$ distance for $p>1$. The results imply that the stability bounds for the logarithmic Sobolev inequality with respect to $W_{1}$, $W_{2}$, and $L^{1}$ in the space of probability measures with bounded second moments are best possible. As an application of the example, we prove instability results for the Beckner--Hirschman inequality in terms of $L^{p}$ distances with specific measures and range of $p$.

Publisher URL: http://arxiv.org/abs/1805.06272

DOI: arXiv:1805.06272v2

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.