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Random walk on a random walk

Author

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  • Kehr, K.W.
  • Kutner, R.

Abstract

The authors investigate the random walk of a particle on a one-dimensional chain which has been constructed by a random-walk procedure. Exact expressions are given for the mean-square displacement and the fourth moment after n steps. The probability density after n steps is derived in the saddle-point approximation, for large n. These quantities have also been studied by numerical simulation. The extension to continuous time has been made where the particle jumps according to a Poisson process. The exact solution for the self-correlation function has been obtained in the Fourier and Laplace domain. The resulting frequency-dependent diffusion coefficient and incoherent dynamical structure factor have been discussed. The model of random walk on a random walk is applied to self-diffusion in the concentrated one-dimensional lattice gas where the correct asymptotic behavior is found.

Suggested Citation

  • Kehr, K.W. & Kutner, R., 1982. "Random walk on a random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(3), pages 535-549.
    • Handle: RePEc:eee:phsmap:v:110:y:1982:i:3:p:535-549
    DOI: 10.1016/0378-4371(82)90067-X
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    References listed on IDEAS

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    1. Kehr, K.W. & Haus, J.W., 1978. "On the equivalence between multistate-trapping and continuous-time random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 93(3), pages 412-426.
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    Cited by:

    1. Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Kutner, Ryszard & Świtała, Filip, 2004. "Remarks on the possible universal mechanism of the non-linear long-term autocorrelations in financial time-series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 244-251.
    3. Balakrishnan, V. & Van den Broeck, C., 1995. "Transport properties on a random comb," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 217(1), pages 1-21.
    4. Spišák, Daniel, 1994. "Two-dimensional diffusion of particles with dipolar-like interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(1), pages 42-50.
    5. Huckaby, Dale A. & Hubbard, Joseph B., 1983. "A random walk on a random channel with absorbing barriers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 602-610.

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