Minimizers for an Aggregation Model with Attractive–Repulsive Interaction
Creators
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1.
Ludwig-Maximilians-Universität München
- 2. Munich Center for Quantum Science and Technology
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3.
California Institute of Technology
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4.
Vanderbilt University
Abstract
We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that in an optimal part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions.
Copyright and License
© The Author(s) (2025). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Acknowledgement
The authors are grateful to D. Bilyk, J. A. Carrillo, D. Chafaï, C. Davies, T. Lim, J. Mateu, R. McCann, E. B. Saff, J. Verdera, M. Vu, and R. Womersley for several discussions, correspondences, and help with references during the process of working on this problem.
Funding
R.L.F. is partially supported through US National Science Foundation grant DMS-1954995, as well as through the Deutsche Forschungsgemeinschaft Excellence Strategy EXC-2111-390814868 and TRR 352 (Project-ID 470903074). R.W.M. is supported by US National Science Foundation Postdoctoral Research Fellowship Grant 2202877.
Open Access funding enabled and organized by Projekt DEAL.
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Additional details
Related works
- Describes
- Journal Article: https://rdcu.be/ew311 (ReadCube)
- Is new version of
- Discussion Paper: arXiv:2307.13769v3 (arXiv)
Funding
- National Science Foundation
- DMS-1954995
- Deutsche Forschungsgemeinschaft
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft
- TRR 352 (Project-ID 470903074)
- National Science Foundation
- DMS-2202877
Dates
- Accepted
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2025-01-15
- Available
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2025-02-11Published online