Mod-φ convergence: Approximation of discrete measures and harmonic analysis on the torus
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Date
2020-01Type
- Journal Article
ETH Bibliography
yes
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Abstract
In this paper, we relate the framework of mod-phi 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 Poisson approximation. This theory applies to various examples arising from combinatorics and number theory: number of cycles in permutations, number of prime divisors of a random integer, number of irreducible factors of a random polynomial, etc. Our approach allows us to deal with approximations in higher dimensions as well. In this setting, we bring out the influence of the correlations between the components of the random vectors in our asymptotic formulas. Show more
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publishedExternal links
Journal / series
Annales de l'Institut FourierVolume
Pages / Article No.
Publisher
Université Joseph FourierSubject
Mod-phi convergence; Wiener algebra; Lattice distributions; Approximation of random variablesMore
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ETH Bibliography
yes
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