Local limit theorems via Landau-Kolmogorov inequalities

Details Local limit theorems via Landau-Kolmogorov inequalities Local limit theorems via Landau-Kolmogorov inequalities

2010-11-13

arxiv.org/abs/1011.3100v2

Mathematics

Probability

major revision; 28 pages

Scientific paper

In this article we use Landau-Kolmogorov inequalities to obtain new inequalities between some common probability metrics. We illustrate the use of these inequalities by providing rates of convergencce in novel local limit theorems for the magnetization in the Curie-Weiss model at high temperature, the number of triangles and isolated vertices in Erdos-Renyi random graphs, as well as the independence number in a geometric random graph. We also obtain new rates of convergence in other probability metrics for some of these examples.

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