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| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Local limit theorems and mod-phi convergence |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | ALEA: Latin American Journal of Probability and Mathematical Statistics |
| Geographical Reach | international |
| Volume | 16 |
| Number | 1 |
| Page Range | 817 - 853 |
| Date | 2019 |
| Abstract Text | We prove local limit theorems for mod-φconvergent sequences of ran-dom variables,φbeing a stable distribution. In particular, we give two new proofsof the local limit theorem stated inDelbaen et al.(2015): one proof based on thenotion ofzone of controlintroduced inFéray et al.(2019+a), and one proof basedon the notion ofmod-φconvergence inL1(iR). These new approaches allow usto identify the infinitesimal scales at which the stable approximation is valid. Wecomplete our analysis with a large variety of examples to which our results ap-ply, and which stem from random matrix theory, number theory, combinatorics orstatistical mechanics. |
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