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Random walk of annihilating particles on the ring

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Abstract

We obtain the formula for the transition probability of an arbitrary number of annihilating particles wandering along a ring-shaped one-dimensional lattice from the initial coordinates to the final coordinates during an arbitrary number of discrete time steps.

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References

  1. M. E. Fisher, J. Stat. Phys., 34, 667 (1984).

    MATH  Google Scholar 

  2. D. A. Huse and M. E. Fisher, Phys. Rev. B, 29, 239 (1984); P. G. de Gennes, J. Chem. Phys., 48, 2257 (1968); J. W. Essam and A. J. Guttmann, Phys. Rev. E, 52, 5849 (1995); A. L. Owczarek, J. W. Essam, and R. Brak, J. Stat. Phys., 102, 997 (2001).

    ADS  MathSciNet  Google Scholar 

  3. I. Gessel and G. Viennot, Adv. Math., 58, 300 (1985).

    Article  MathSciNet  Google Scholar 

  4. C. Krattenthaler, A. J. Guttmann, and X. G. Viennot, J. Phys. A, 31, 8123 (1998); 33, 8835 (2000).

    ADS  MathSciNet  Google Scholar 

  5. R. Brak, J. W. Essam, and A. L. Owczarek, Ann. Comb., 3, 251 (1999); R. Brak and A. L. Owczarek, J. Phys. A, 32, 3497 (1999).

    MathSciNet  Google Scholar 

  6. R. Baxter, Exactly Solved Models in Statistical Mechanics, Acad. Press, London (1982).

    Google Scholar 

  7. F. Spitzer, Principles of Random Walk (Univ. Ser. in Higher Math.), Van Nostrand, Princeton, N. J. (1964).

    Google Scholar 

  8. E. E. Beckenbach, Applied Combinatorial Mathematics, Wiley, New York (1964).

    Google Scholar 

  9. W. Feller, An Introduction to Probability Theory and Its Applications, Vols. 1, 2, Wiley, New York (1970, 1971).

    Google Scholar 

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 488–498, March, 2006.

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Grigoriev, S.Y., Priezzhev, V.B. Random walk of annihilating particles on the ring. Theor Math Phys 146, 411–420 (2006). https://doi.org/10.1007/s11232-006-0049-x

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  • DOI: https://doi.org/10.1007/s11232-006-0049-x

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