On the Supremum of Some Random Dirichlet Polynomials

TL;DR

This paper investigates the maximum size of certain random Dirichlet polynomials with independent coefficients, providing precise bounds on their expected supremum using stochastic process techniques.

Contribution

It extends previous results by deriving sharp bounds for the supremum of random Dirichlet polynomials through metric entropy methods.

Findings

Established sharp upper bounds for the supremum expectation.

Derived sharp lower bounds for the supremum expectation.

Extended previous work on random Dirichlet polynomials.

Abstract

We study the supremum of some random Dirichlet polynomials with independent coefficients and obtain sharp upper and lower bounds for supremum expectation thus extending the results from our previous work (see http://arXiv.org/abs/math/0703691). Our approach in proving these results is entirely based on methods of stochastic processes, in particular the metric entropy method.