Seminario de Probabilidad para Estudiantes de Posgrado

Jueves 28 de octubre de 2021
09:00hrs

En línea (Zoom)


Imparte(n)

  • Arturo Jaramillo Gil
    (CIMAT)

Responsable(s):

  • Adrián González-Casanova Soberón

Resumen:

We present a new perspective of assessing the rates of convergence to the Gauss- ian and Poisson distributions in the Erdos-Kac theorem for additive arithmetic functions ψ of a random integer Jn uniformly distributed over {1, ..., n}. Our approach is probabilistic, working directly on spaces of random variables without any use of Fourier analytic meth- ods, and our ψ is more general than those considered in the literature. Our main results are (i) bounds on the Kolmogorov distance and Wasserstein distance between the distribution of the normalized ψ(Jn) and the standard Gaussian distribution, and (ii) bounds on the Kolmogorov distance and total variation distance between the distribution of ψ(Jn) and a Poisson distribution under mild additional assumptions on ψ. Our results generalize the existing ones in the literature


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