Examinando por Autor "Cortez, Roberto"

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    Ítem
    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.
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    Uniform propagation of chaos for a dollar exchange econophysics model
    (Publisher Cambridge University Press, 2024) Cao, Fei; Cortez, Roberto
    We study the poor-biased model for money exchange introduced in Cao & Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.): agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random. Simulations of a stochastic system of finitely many agents as well as a rigorous analysis carried out in Cao & Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.), Lanchier ((2017) J. Stat. Phys. 167(1), 160–172.) suggest that, when both the number of agents and time become large enough, the distribution of money among the agents converges to a Poisson distribution. In this manuscript, we establish a uniform-in-time propagation of chaos result as the number of agents goes to infinity, which justifies the validity of the mean-field deterministic infinite system of ordinary differential equations as an approximation of the underlying stochastic agent-based dynamics. © The Author(s), 2024.