Skip to main content
Log in

Relating microscopic and macroscopic parameters for a 3-dimensional random walk

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider a particle undergoing a discrete random walk with killing. We relate the microscopic transition and killing probabilities to these same parameters at a macroscopic level. We find the appropriate scaling laws.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Schroder, E.: Über iterierte Funktionen. Math. Ann.2, 317–365 (1870)

    Google Scholar 

  2. Poincaré, H.: Oeuvres, Vol. 1, pp. XCIV–CV of Thesis

  3. Koenigs, G.: Recherches sur les intégrales de certaines équations fonctionnelles. Ann. Sci. École Norm. Sup. Supp. 3–41 (1984)

  4. Lévy, P.: Fonctions à croissance régulière et itération d'ordre fractionnaire. Ann. Mat. Pura Appl5, 269–298 (1928)

    Google Scholar 

  5. Leau, L.: Etude sur les equations fonctionelle a une ou plusieurs variables. Annales de la Faculte des Sciences de Toulouse 11, E.1-E.110 (1987)

    Google Scholar 

  6. Sternberg, S.: Local contractions and a theorem of Poincaré, Am. J. Math.79, 809–824 (1957)

    Google Scholar 

  7. Hartman, P.: Ordinary differential equations. New York: Wiley 1964

    Google Scholar 

  8. Kato, T.: Perturbation theory of linear operators. Berlin, Heidelberg, New York: Springer 1966

    Google Scholar 

  9. Nelson, E.: Topics in dynamics. Princeton, NJ: Princeton University Press 1968–1969

    Google Scholar 

  10. Grünbaum, F. A.: On the existence of a “wave operator” for the Boltzmann equation, Bull. Am. Math. Soc.78, 759–762 (1972)

    Google Scholar 

  11. Grünbaum, F. A.: Renormalization of exit probabilities and a theorem of Poincaré. To appear in Physics Letters A

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Jaffe

Research partially supported by NSF under Grant DMS 87-20007 and AFOSR under contract AFOSR-88-0250

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grünbaum, F.A. Relating microscopic and macroscopic parameters for a 3-dimensional random walk. Commun.Math. Phys. 129, 95–102 (1990). https://doi.org/10.1007/BF02096780

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096780

Keywords

Navigation