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Mod-$\phi $ convergence: Approximation of discrete measures and harmonic analysis on the torus
In this paper, we relate the framework of mod-convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is the one of Fourier analysis in the Wiener algebra, allowing the computation of asymptotic equivalents of the local, Kolmogorov and total variation distances. By using signed measures instead of probability measures, we are able to construct better approximations of discrete lattice distributions than the standard Poissondoi:10.5167/uzh-190760 fatcat:ksltbpvtsnbkxi4leande6mwaa