From convergence in distribution to uniform convergence

J. M. Bogoya, A. Böttcher, E. A. Maximenko

Resultado de la investigación: Contribución a una revistaArtículo

5 Citas (Scopus)

Resumen

© 2016 Sociedad Matemática Mexicana. We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic distribution of collections of real numbers, such as the eigenvalues of a family of n-by-n matrices as n goes to infinity, to their uniform approximation by the values of the quantile function at equidistant points. For Hermitian Toeplitz-like matrices, convergence in distribution is ensured by theorems of the Szeg o type. Our results transfer these convergence theorems into uniform convergence statements.
Idioma originalInglés estadounidense
PublicaciónBoletin de la Sociedad Matematica Mexicana
DOI
EstadoPublicada - 1 oct 2016

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