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arXiv · 1710.10679

Local limit theorems and mod-phi convergence

Martina dal Borgo·Pierre-Loïc Méliot·Ashkan Nikeghbali
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Abstract

We prove local limit theorems for mod-{\phi} convergent sequences of random variables, {\phi} being a stable distribution. In particular, we give two new proofs of a local limit theorem in the framework of mod-phi convergence: one proof based on the notion of zone of control, and one proof based on the notion of mod-{\phi} convergence in L1(iR). These new approaches allow us to identify the infinitesimal scales at which the stable approximation is valid. We complete our analysis with a large variety of examples to which our results apply, and which stem from random matrix theory, number theory, combinatorics or statistical mechanics.

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Martina dal Borgo, Pierre-Loïc Méliot, Ashkan Nikeghbali. 2017-10-29. Local limit theorems and mod-phi convergence. https://arxiv.org/abs/1710.10679

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