Article
Supremum of Random Dirichlet Polynomials With Sub-Multiplicative Coefficients
Authors
Abstract
We study the supremum of random Dirichlet polynomials
\[
D_N(s)=\sum_{n=1}^{N}\varepsilon_n d(n)n^{-s},
\]
where \((\varepsilon_n)\) is a sequence of independent Rademacher random variables, and \(d\) is a sub-multiplicative function. The approach is Gaussian and entirely based on comparison properties of Gaussian processes, with no use of the metric entropy method. As in preceding related works, the proof uses a sieve argument due to Queffélec.
Keywords
RandomDirichletpolynomials, sub-multiplicative coefficients, maximum, Gaussian processes.
Citation
Weber, M. (2010). Supremum of random dirichlet polynomials with sub-multiplicative coefficients. Uniform Distribution Theory, 5(1), 163–197.
M. Weber, “Supremum of random dirichlet polynomials with sub-multiplicative coefficients,” Uniform Distribution Theory, vol. 5, no. 1, pp. 163–197, 2010.
Weber M. Supremum of random dirichlet polynomials with sub-multiplicative coefficients. Uniform Distribution Theory. 2010;5(1):163–197.
Weber, M. (2010), ‘Supremum of random dirichlet polynomials with sub-multiplicative coefficients’, Uniform Distribution Theory, 5(1), pp. 163–197.
Weber, Michel. “Supremum of Random Dirichlet Polynomials with Sub-multiplicative Coefficients.” Uniform Distribution Theory, vol. 5, no. 1, 2010, pp. 163–197.
Weber, Michel. “Supremum of Random Dirichlet Polynomials with Sub-multiplicative Coefficients.” Uniform Distribution Theory 5, no. 1 (2010): 163–197.
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Published by: Engineering Journals
