Advertisement

Communications in Mathematical Physics

, Volume 112, Issue 2, pp 217–235 | Cite as

Correlations of peaks of Gaussian random fields

  • James M. Cline
  • H. David Politzer
  • Soo-Jong Rey
  • Mark B. Wise
Article

Abstract

The high peaks of a Gaussian random field are studied. Asymptotic expansions, appropriate for high peak thresholds and large spatial separations, are developed for theN-point correlation functions of the number density of high peaks, in terms of the two-point correlation of the underlying Gaussian field. Similar expressions are derived for the correlations of points, not necessarily the positions of peaks, where the field exceeds a high threshold.

Keywords

Neural Network Statistical Physic Correlation Function Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rice, S. O.: Mathematical analysis of random noise. In: Selected papers on noise and stochastic processes. New York: Dover 1954Google Scholar
  2. 2.
    Kaiser, N.: Ap. J.284, L9 (1984)Google Scholar
  3. 3.
    Bardeen, J. M., Bond, J. R., Kaiser, N., Szalay, A. S.: Ap. J.304, 15 (1986)Google Scholar
  4. 4.
    Politzer, H. D., Wise, M. B.: Ap. J.285, L1 (1984)Google Scholar
  5. 5.
    Jensen, L. G., Szalay, A. S.: Ap. J.305, L5 (1986)Google Scholar
  6. 6.
    Berezin, F. A.: The method of second quantization. New York, London: Academic Press 1966Google Scholar
  7. 7.
    Adler, R. J.: The geometry of random fields. New York: Wiley 1981Google Scholar
  8. 8.
    Doroshkevich, A. G.: Astrophysics6, 320 (1970)Google Scholar
  9. 9.
    Otto, S., Politzer, H. D., Wise, M. B.: Phys. Rev. Lett.56, 1978 (1986)Google Scholar
  10. 10.
    Mirsky, L.: An introduction to linear algebra. Oxford: Oxford University Press 1963Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • James M. Cline
    • 1
  • H. David Politzer
    • 1
  • Soo-Jong Rey
    • 1
  • Mark B. Wise
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

Personalised recommendations