Journal of Theoretical Probability

, Volume 9, Issue 4, pp 1019–1027 | Cite as

Zero-one laws for polynomials in Gaussian random variables: A simple proof

  • P. Heinrich
Article

Abstract

Zero-one laws for polynomials in Gaussian random variables have already been studied.(7) They are established here by very simple arguments: Fubini's theorem and the rotational invariance of centered Gaussian measures. The proof is built on the Polarization formula that has received much attention in Refs. 1 and 5. Our point of view derives from the deep work of Borell.(2) In a natural way, these results extend to finite-order Gaussian chaos processes.

Key Words

Gaussian measures Gaussian chaos zero-one laws 

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References

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • P. Heinrich
    • 1
  1. 1.Département de MathématiquesUniversité Louis PasteurStrasbourg CedexFrance

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