Skip to main content
SpringerLink
Log in

Twice Scattered Particles in a Plane Are Uniformly Distributed

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

Abstract

It was recently shown (Physica A 216:299–315, 1995) that in two dimensions the sum of three vectors each of whose lengths is exponentially distributed, whose direction is uniformly distributed and such that the sum of their lengths is l, is uniformly distributed on a disk of radius l. We state here this random walk result in terms of scattering of particles as follows: in two dimensions twice isotropically scattered particles by random (i.e., Poisson distributed) scatterers are uniformly distributed. We show that there is no other dimension d and no other number of scatterings s for which the corresponding result (i.e., uniform distribution on a d-dimensional sphere after s scatterings) holds.

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

References

  1. García-Pelayo, R.: Moments of the chain reaction distribution. Physica A 216, 299–315 (1995)

    Article  ADS  Google Scholar 

  2. Franceschetti, M.: When a random walk of fixed length can lead uniformly anywhere inside a hypersphere. J. Stat. Phys. 127, 813–823 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. Goldstein, S.: On diffusion by discontinuous movements, and on the telegraph equation. Quart. J. Mech. Appl. Math. IV, Pt. 2, 129–156 (1951)

    Article  Google Scholar 

  4. Masoliver, J., Porrá, J.M., Weiss, G.H.: Some two and three-dimensional persistent random walks. Physica A 193, 469–482 (1993)

    Article  ADS  Google Scholar 

  5. García-Pelayo, R.: Multiple scattering. Physica A 258, 365–382 (1998)

    Article  Google Scholar 

  6. Slomson, A.: An Introduction to Combinatorics. Chapman Hall, London (1991)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ETS de Ingeniería Aeronáutica, Universidad Politécnica de Madrid, Plaza del Cardenal Cisneros, 3, Madrid, 28040, Spain

    Ricardo García-Pelayo

Authors
  1. Ricardo García-Pelayo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ricardo García-Pelayo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

García-Pelayo, R. Twice Scattered Particles in a Plane Are Uniformly Distributed. J Stat Phys 133, 401–404 (2008). https://doi.org/10.1007/s10955-008-9612-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-008-9612-1

Keywords

Search

Navigation