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Quantitative Stability Of Aggregation-Diffusion Under Local Attraction

  • Yunhong Deng
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Abstract

In this note, we establish quantitative stability of aggregation-diffusion energy for compactly supported data. Our consideration focuses on the degenerate diffusion with local attraction that are asymptotically flat at infinity, such as Riesz kernels. We characterize the spectrum lower-bound of the Wasserstein Hessian at steady states. Assumptions are kept as minimal as that needed for uniqueness.

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Cite

BibTeXRIS
BibTeX
@misc{deng2026quantitative,
  title = {{Quantitative Stability Of Aggregation-Diffusion Under Local Attraction}},
  author = {Yunhong Deng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07264},
  eprint = {2610.07264},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07264},
}
RIS
TY  - UNPB
TI  - Quantitative Stability Of Aggregation-Diffusion Under Local Attraction
AU  - Yunhong Deng
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07264
UR  - https://arxiv.org/abs/2610.07264
AB  - In this note, we establish quantitative stability of aggregation-diffusion energy for compactly supported data. Our consideration focuses on the degenerate diffusion with local attraction that are asymptotically flat at infinity, such as Riesz kernels. We characterize the spectrum lower-bound of the Wasserstein Hessian at steady states. Assumptions are kept as minimal as that needed for uniqueness.
ER  -