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Fourth Moments and Products: Unified Estimates

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Convexity and Concentration

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

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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.

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References

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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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Authors and Affiliations

  1. Université du Luxembourg, Esch-sur-Alzette, Luxembourg

    Ivan Nourdin & Giovanni Peccati

Authors
  1. Ivan Nourdin
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  2. Giovanni Peccati
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Corresponding author

Correspondence to Ivan Nourdin .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Rutgers University, Piscataway, New Jersey, USA

    Eric Carlen

  2. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    Mokshay Madiman

  3. Department of Mathematics, Case Western Reserve University, Cleveland, Ohio, USA

    Elisabeth M. Werner

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Nourdin, I., Peccati, G. (2017). Fourth Moments and Products: Unified Estimates. In: Carlen, E., Madiman, M., Werner, E. (eds) Convexity and Concentration. The IMA Volumes in Mathematics and its Applications, vol 161. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7005-6_10

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