Not logged in.
Quick Search - Contribution
Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Mod-$\phi $ convergence: Approximation of discrete measures and harmonic analysis on the torus |
| Organization Unit | |
| Authors |
|
| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
|
| Journal Title | Annales de l'Institut Fourier |
| Publisher | Association des Annales de l'Institut Fourier |
| Geographical Reach | international |
| ISSN | 0373-0956 |
| Volume | 70 |
| Number | 3 |
| Page Range | 1115 - 1197 |
| Date | 2020 |
| Abstract Text | In this paper, we relate the framework of mod-φ 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. |
| Free access at | DOI |
| Digital Object Identifier | 10.5802/aif.3332 |
| Other Identification Number | merlin-id:19436 |
| PDF File |
Download from ZORA
|
| Export |
BibTeX
EP3 XML (ZORA)
|