Fourth Moments and Products: Unified Estimates

Conference paper
First Online:
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 161)

Abstract

We provide a unified discussion, based on the properties of eigenfunctions of the generator of the Ornstein-Uhlenbeck semigroup, of quantitative fourth moment theorems and of the weak Gaussian product conjecture. In particular, our approach illustrates the connections between moment estimates for non-linear functionals of Gaussian fields, and the general semigroup approach towards fourth moment theorems, recently initiated by Ledoux and further investigated by Poly et al.

Keywords

Fourth moment theorem Gaussian fields Gaussian vectors Moment inequalities Ornstein-Uhlenbeck semigroup Polarization conjecture Probabilistic approximations Variance inequalities Wiener chaos 
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Notes

Acknowledgements

We thank an anonymous referee for insightful comments.

IN is partially supported by the grant F1R-MTH-PUL-15CONF (CONFLUENT) at Luxembourg University.

GP is partially supported by the grant F1R-MTH-PUL-15STAR (STARS) at Luxembourg University.

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Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Université du LuxembourgEsch-sur-AlzetteLuxembourg

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