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An extended deviation result from bounds on cumulants

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Mod-ϕ Convergence

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Abstract

In this chapter, we discuss a particular case of mod-Gaussian variables that arises from bounds on cumulants. We will see that in this case the deviation result given in Theorem 4.2.1 is still valid at a scale larger than t n ; see Proposition 5.2.1.

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Bibliography

  1. V. Féray, P.-L. Méliot, and A. Nikeghbali. Mod-φ convergence, II: Estimates of the speed of convergence and local limit theorems. In preparation, 2016.

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  2. R. Rudzkis, L. Saulis, and V. A. Statulevičius. A general lemma for large deviations. Lithuanian Math. J., 18:99–116, 1978.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich — Winterthurerstrasse, Zürich, Switzerland

    Valentin Féray & Ashkan Nikeghbali

  2. Laboratoire de Mathématiques, Bâtiment 425 — Faculté Des Sciences, d’Orsay—Université Paris-Sud, Orsay, France

    Pierre-Loïc Méliot

Authors
  1. Valentin Féray
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  2. Pierre-Loïc Méliot
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  3. Ashkan Nikeghbali
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Féray, V., Méliot, PL., Nikeghbali, A. (2016). An extended deviation result from bounds on cumulants. In: Mod-ϕ Convergence. SpringerBriefs in Probability and Mathematical Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-46822-8_5

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