Skip to main content
SpringerLink
Log in

Coordinates Changed Random Fields on the Sphere

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential equations with random initial condition represented by a Gaussian random field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baldi, P., Marinucci, D.: Some characterization of the spherical harmonics coefficients for isotropic random fields. Stat. Probab. Lett. 77, 490–496 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D.: High-frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus. J. Multivar. Anal. 99, 606–636 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bartolo, N., Komatsu, E., Matarrese, S., Riotto, A.: Non-Gaussianity from inflation: theory and observations. Phys. Rep. 402, 103–266 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  4. Dodelson, S.: Modern Cosmology. Academic Press, Amsterdam (2003)

    Google Scholar 

  5. D’Ovidio, M., Nane, E.: Time dependent random fields on spherical non-homogeneous surfaces. arXiv. 1205.6280v2 (submitted)

  6. D’Ovidio, M.: Explicit solutions to fractional diffusion equations via generalized gamma convolution. Electron. Commun. Probab. 15, 457–474 (2010)

    MATH  MathSciNet  Google Scholar 

  7. D’Ovidio, M.: From Sturm–Liouville problems to fractional and anomalous diffusions. Stoch. Process Appl. 122, 3513–3544 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hu, W., White, M.: The Cosmic Symphony. Scientific American, pp. 44–53 (2004)

  9. Kampé de Fériet, J.: Random solutions of partial differential equations. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 3, pp. 199–208. University of California Press, Berkeley (1956)

  10. Kolb, E., Turner, M.: The Early Universe. Cambridge University Press, Cambridge (1994)

    Google Scholar 

  11. Komatsu, H.: Fractional powers of operators. Pac. J. Math. 19, 285–346 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kravvaritis, D.: Random semilinear evolution equations in Banach spaces. Proc. Am. Math. Soc. 113, 715–722 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  13. Marinucci, D.: High resolution asymptotics for the angular bispectrum of spherical random fields. Ann. Stat. 34, 1–41 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Marinucci, D., Peccati, G.: High-frequency asymptotics for subordinated isotropic fields on an abelian compact group. Stoch. Proc. Appl. 118, 585–613 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Marinucci, D., Peccati, G.: Ergodicity and Gaussianity for spherical random fields. J. Math. Phys. 52, 043301 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  16. Marinucci, D., Peccati, G.: Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications. Cambridge University Press, Cambridge (2011)

    Book  Google Scholar 

  17. Nane, E.: Fractional Cauchy problems on bounded domains: survey of recent results. In: Baleanu, D., Machado, J.A.T., Luo, A.C.J. (eds.) Fractional Dynamics and Control, pp. 185–198. Springer, New York (2012)

    Chapter  Google Scholar 

  18. Varshalovich, D.A., Moskalev, A.N., Khersonskii, V.K.: Quantum Theory of Angular Momentum. World Scientific Publishing Co., Pte. Ltd., Singapore (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza University of Rome, A. Scarpa 10, 00161 , Rome, Italy

    Mirko D’Ovidio

Authors
  1. Mirko D’Ovidio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mirko D’Ovidio.

Rights and permissions

Reprints and permissions

About this article

Cite this article

D’Ovidio, M. Coordinates Changed Random Fields on the Sphere. J Stat Phys 154, 1153–1176 (2014). https://doi.org/10.1007/s10955-013-0911-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-013-0911-9

Keywords

Search

Navigation