Abstract
We discuss a natural extension of Gilles Pisier’s approach to the study of measure concentration, isoperimetry, and Poincaré-type inequalities. This approach allows one to explore counterparts of various results about Gaussian measures in the class of rotationally invariant probability distributions on Euclidean spaces, including multidimensional Cauchy measures.
Funding Statement
Research of S.B. was partially supported by the NSF grant DMS-2154001. B.V. was partially supported by Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of Istituto Nazionale di Alta Matematica (INdAM). This study was also carried out within the “Geometric-Analytic Methods for PDEs and Applications (GAMPA)” projects – funded by the Ministero dell’Università e della Ricerca – within the PRIN 2022 program (D.D.104 – 02/02/2022). This manuscript reflects only the authors’ views and opinions and the Ministry cannot be considered responsible for them.
Acknowledgments
We would like to thank the referee for a very careful reading of the manuscript and numerous remarks and suggestions improving this paper. This work was started in 2018 when B.V. visited to the University of Minnesota and was continued in 2022 when S.B. visited to the Parthenope University of Naples. The authors are grateful for hospitality.
Citation
Sergey G. Bobkov. Bruno Volzone. "On Gilles Pisier’s approach to Gaussian concentration, isoperimetry, and Poincaré-type inequalities." Electron. J. Probab. 29 1 - 27, 2024. https://doi.org/10.1214/24-EJP1104
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