Repositorio Institucional Académico. Universidad Andrés Bello. Chile

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Chaos for rescaled measures on Kac’s sphere
(Institute of Mathematical Statistics, 2023) Cortez, Roberto; Tossounian, Hagop
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.