Abstract
We study the average supremum of some random Dirichlet polynomials D N (t) = Σ N n=1 ɛ n d(n)n −σ−it, where (ɛ n ) is a sequence of independent Rademacher random variables, the weights d(n) satisfy some reasonable conditions and 0 ≦ σ ≦ 1/2. We use an approach based on methods of stochastic processes, in particular the metric entropy method developed in [8].
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Lifshits, M., Weber, M. On the supremum of some random Dirichlet polynomials. Acta Math Hung 123, 41–64 (2009). https://doi.org/10.1007/s10474-008-8059-9
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DOI: https://doi.org/10.1007/s10474-008-8059-9