Chaos for rescaled measures on Kac’s sphere
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2023
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en
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Institute of Mathematical Statistics
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Licencia CC
CC BY 4.0 DEED Attribution 4.0 International
Licencia CC
https://creativecommons.org/licenses/by/4.0/
Resumen
In this article we study a relatively novel way of constructing chaotic sequences of probability measures supported on Kac’s sphere, which are obtained as the law of a vector of N i.i.d. variables after it is rescaled to have unit average energy. We show that, as N increases, this sequence is chaotic in the sense of Kac, with respect to the Wasserstein distance, in L1, in the entropic sense, and in the Fisher information sense. For many of these results, we provide explicit rates of polynomial order in N. In the process, we improve a quantitative entropic chaos result of Haurey and Mischler by relaxing the finite moment requirement on the densities from order 6 to 4 + ɛ. © 2023, Institute of Mathematical Statistics. All rights reserved.
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Indexación: Scopus
Funding Statement R. Cortez was supported by ANID Fondecyt Iniciación Grant 11181082. H. Tossounian was supported by ANID Fondecyt Postdoctoral Grant 3200130, and Centro de Modelamiento Matemático (CMM) BASAL fund FB210005 for center of excellence from ANID-Chile. Acknowledgments We thank the two anonymous referees who provided insightful comments and suggestions that allowed us to improve the presentation of this article
Funding Statement R. Cortez was supported by ANID Fondecyt Iniciación Grant 11181082. H. Tossounian was supported by ANID Fondecyt Postdoctoral Grant 3200130, and Centro de Modelamiento Matemático (CMM) BASAL fund FB210005 for center of excellence from ANID-Chile. Acknowledgments We thank the two anonymous referees who provided insightful comments and suggestions that allowed us to improve the presentation of this article
Palabras clave
Entropic chaos, Entropy, Fisher information, Kac’s chaos, Propagation of chaos
Citación
Electronic Journal of Probability. Volume 28. 2023. Article number 80
DOI
10.1214/23-EJP967