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May 2015 Local limit theorems via Landau–Kolmogorov inequalities
Adrian Röllin, Nathan Ross
Bernoulli 21(2): 851-880 (May 2015). DOI: 10.3150/13-BEJ590


In this article, we prove new inequalities between some common probability metrics. Using these inequalities, we obtain novel local limit theorems for the magnetization in the Curie–Weiss model at high temperature, the number of triangles and isolated vertices in Erdős–Rényi random graphs, as well as the independence number in a geometric random graph. We also give upper bounds on the rates of convergence for these local limit theorems and also for some other probability metrics. Our proofs are based on the Landau–Kolmogorov inequalities and new smoothing techniques.


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Adrian Röllin. Nathan Ross. "Local limit theorems via Landau–Kolmogorov inequalities." Bernoulli 21 (2) 851 - 880, May 2015.


Published: May 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1320.60065
MathSciNet: MR3338649
Digital Object Identifier: 10.3150/13-BEJ590

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability


Vol.21 • No. 2 • May 2015
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