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Journal of Statistical Physics

, Volume 58, Issue 1–2, pp 159–183 | Cite as

Monte Carlo generation of self-avoiding walks with fixed endpoints and fixed length

  • N. Madras
  • A. Orlitsky
  • L. A. Shepp
Articles

Abstract

We propose a new class of dynamic Monte Carlo algorithms for generating self-avoiding walks uniformly from the ensemble with fixed endpoints and fixed length in any dimension, and prove that these algorithms are ergodic in all cases. We also prove the ergodicity of a variant of the pivot algorithm.

Key words

Self-avoiding walk self-avoiding polygon Monte Carlo ergodicity pivot algorithm 

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References

  1. 1.
    C. Domb,Adv. Chem. Phys. 15:229 (1969).Google Scholar
  2. 2.
    S. G. Whittington,Adv. Chem. Phys. 51:1 (1982).Google Scholar
  3. 3.
    P. G. de Gennes,Phys. Lett. A 38:339 (1972).Google Scholar
  4. 4.
    K. Kremer and K. Binder,Comp. Phys. Rep. 7:259 (1988).Google Scholar
  5. 5.
    N. Madras and A. D. Sokal,J. Stat. Phys. 47:573 (1987).Google Scholar
  6. 6.
    M. Lal,Mol. Phys. 17:57 (1969).Google Scholar
  7. 7.
    N. Madras and A. D. Sokal,J. Stat. Phys. 50:109 (1988).Google Scholar
  8. 8.
    B. Berg and D. Foerster,Phys. Lett. 106B:323 (1981).Google Scholar
  9. 9.
    C. Aragão de Carvalho, S. Caracciolo, and J. Fröhlich,Nucl. Phys. B 215[FS7]:209 (1983).Google Scholar
  10. 10.
    C. Aragão de Carvalho and S. Caracciolo,J. Phys. (Paris)44:323 (1983).Google Scholar
  11. 11.
    A. D. Sokal and L. E. Thomas,J. Stat. Phys. 51:907 (1988).Google Scholar
  12. 12.
    L. E. Dubins, A. Orlitsky, J. A. Reeds, and L. A. Shepp,IEEE Trans. Inform. Theory 34:1509 (1988).Google Scholar
  13. 13.
    A. Berretti and A. D. Sokal,J. Stat. Phys. 40:483 (1985).Google Scholar
  14. 14.
    S. Caracciolo, A. Pelissetto, and A. D. Sokal, preprint.Google Scholar
  15. 15.
    S. Karlin and H. M. Taylor,A First Course in Stochastic Processes (Academic Press, New York, 1975).Google Scholar
  16. 16.
    B. MacDonald, N. Jan, D. L. Hunter, and M. O. Steinitz,J. Phys. A: Math. Gen. 18:2627 (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • N. Madras
    • 1
  • A. Orlitsky
    • 2
  • L. A. Shepp
    • 2
  1. 1.Department of MathematicsYork UniversityNorth YorkCanada
  2. 2.AT & T Bell LaboratoriesMurray Hill

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