Discrepancy for randomized riemann sums

Luca Brandolini*, William Chen, Giacomo Gigante, Giancarlo Travaglini

*Corresponding author for this work

    Research output: Contribution to journalArticle

    2 Citations (Scopus)
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    Abstract

    Given a finite sequence UN = {u1,., uN} of points contained in the d-dimensional unit torus, we consider the L2 discrepancy between the integral of a given function and the Riemann sums with respect to translations of UN. We show that with positive probability, the L2 discrepancy of other sequences close to UN in a certain sense preserves the order of decay of the discrepancy of UN. We also study the role of the regularity of the given function.

    Original languageEnglish
    Pages (from-to)3187-3196
    Number of pages10
    JournalProceedings of the American Mathematical Society
    Volume137
    Issue number10
    DOIs
    Publication statusPublished - Oct 2009

    Bibliographical note

    Copyright 2009 American Mathematical Society. First published in Proceedings of the American Mathematical Society, Volume 137, Issue 10, pp. 3187-3196, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0002-9939-09-09975-4.

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  • Cite this

    Brandolini, L., Chen, W., Gigante, G., & Travaglini, G. (2009). Discrepancy for randomized riemann sums. Proceedings of the American Mathematical Society, 137(10), 3187-3196. https://doi.org/10.1090/S0002-9939-09-09975-4