@article{StabilityWavelets,
    author = {Gómez, Jaime and Kalaj, David and Melentijević, Petar and Ramos, João P. G.},
    title = {Uniform stability of concentration inequalities and applications},
    journal = {Proceedings of the London Mathematical Society},
    volume = {131},
    number = {6},
    pages = {e70114},
    doi = {https://doi.org/10.1112/plms.70114},
    url = {https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms.70114},
    eprint = {https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/plms.70114},
    abstract = {Abstract We prove a sharp quantitative version of recent Faber-Krahn inequalities for the continuous Wavelet transforms associated to a certain family of Cauchy wavelet windows [Ramos and Tilli, Soc. 55 (2023), no. 4, 2018-2034]. Our results are uniform on the parameters of the family of Cauchy wavelets, and asymptotically sharp in both directions. As a corollary of our results, we are able to recover not only the original result for the short-time Fourier transform as a limiting procedure, but also a new concentration result for functions in Hardy spaces. This is a completely novel result about optimal concentration of Poisson extensions, and our proof automatically comes with a sharp stability version of that inequality. Our techniques highlight the intertwining of geometric and complex-analytic arguments involved in the context of concentration inequalities. In particular, in the process of deriving uniform results, we obtain a refinement over the proof of the result in [Gómez et al., Invent. Math. 236 (2024), no. 2, 779-836], further improving the current understanding of the geometry of near extremals in all contexts under consideration.},
    year = {2025}
}