Scaling Limits of Generalized Random Processes

  • Volker Enss
Conference paper


In Dobrushin’s setup of scale transformations with multiplicative renormalization for generalized random processes we study the Short- and long-distance behaviour of various processes, in particular of Wick-polynomials of Gaussian fields and of P(ф)2-models from constructive quantum field theory.


White Noise Gaussian Process Curly Bracket Gaussian Field Massless Field 


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  1. [1]
    Chung, K.L.: A course in probability theory, New York, Academic Press 1974.MATHGoogle Scholar
  2. [2] a)
    Dobrushin, R.L.: Automodel generalized random fields and their renorm-group. In: Multicomponent Random Systems. Dekker, New York, to appear.Google Scholar
  3. [2] b)
    Dobrushin, R.L Ann. Prob. 7, 1–28 (1979)CrossRefMATHMathSciNetGoogle Scholar
  4. [3]
    Enss, V.: Rep. Math. Phys. V3, 87–99 (1978).CrossRefADSGoogle Scholar
  5. [4]
    Enss, V.: Random processes converging to white noise, in preparation.Google Scholar
  6. [5]
    Gel’fand, I.M., Vilenkin, N.Ya.: Generalized functions Vol. IV, New York, Academic Press 1964.MATHGoogle Scholar
  7. [6]
    Haba, Z.: Scale limit and low momentum behaviour of Eudli- dean fields II., preprint Bielefeld BI-TP 78/25.Google Scholar
  8. [7]
    Hida, T. Proc. Japan Acad. 54, SerA, 55–58 (1978).MathSciNetGoogle Scholar
  9. [8]
    Ibragimov I.A., Linnik, Yu.V.: Independent and stationary sequences of random variables, Groningen, Wolters-Noordhoff 1971.MATHGoogle Scholar
  10. [9]
    Jona-Lasinio, G.: in “New developments in quantum field theory and Statistical mechanics - Cargese 1976”, M. Levy and P. Mitter ed., New York, Plenum 1977.Google Scholar
  11. [10]
    Karwowski, W., Streit, L.: Rep. Math. Phys 13, 1–12 (1978).CrossRefMATHADSMathSciNetGoogle Scholar
  12. [11]
    Velo, G., Wightman, A. ed.: Constructive quantum field theory, Lecture Notes in Physics 25, Berlin, Springer 1973.Google Scholar
  13. [12]
    Eckmann, J.P., Magnen, J., Seneor, R.: Commun. Math. Phys. 39, 251–271 (1975);CrossRefADSMathSciNetGoogle Scholar
  14. Glimm, J., Jaffe, A., Spencer, T.: Ann. Phys. (N.Y.) 101, 610–630, 631–669 (1976);CrossRefADSMathSciNetGoogle Scholar
  15. Fröhlich, J.: Adv. Math. 23, 119–180 (1977).CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1980

Authors and Affiliations

  • Volker Enss
    • 1
  1. 1.Fakultät für PhysikUniversität BielefeldBielefeldFederal Republic of Germany

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