for this workshop
Entropy power inequalities
American Institute of Mathematics, San Jose, California
Andrew Barron, Dongning Guo, Oliver Johnson, and Ioannis Kontoyiannis
This workshop, sponsored by AIM and the NSF, will be devoted to bringing together researchers from different communities (including probability, functional analysis, information and estimation theory), who study and use forms of Shannon's Entropy Power Inequality (EPI). This result and its many extensions and generalizations have been proved using a number of different approaches, including the de Bruijn identity, optimal transport and minimum mean square estimation (MMSE). Although the EPI is interesting in its own right, it has further significant impact by connecting several important and active research areas, including functional inequalities on Riemannian manifolds, inequalities in convex geometry, entropic versions of results in additive combinatorics and bounding the capacity of communication channels.
The main topics for the workshop are to:
- Understand and help unify the existing approaches to the EPI, and related results including reverse EPIs, forms of log-Sobolev inequalities and sumset bounds in additive combinatorics.
- Develop new EPIs in infinitely divisible settings, to include stable laws and integer-valued variables.
- Establish new connections arising from these methods.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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