Abstract
A restricted random walk on ad-dimensional cubic lattice with different probabilities for forward, backward, and sideward steps is studied. The analytic solution for the generating function, exact expressions for the second and fourth moments of displacements, and diffusion and Burnett coefficients are given, as well as a systematic asymptotic expansion for the probability distribution of long walks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. G. van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
J. W. Haus and K. W. Kehr,Phys. Rep. 50:263 (1987), Section 4.
P. M. Binder,Complex Systems 1:559 (1987); M. H. Ernst and P. M. Binder,J. Stat. Phys. (1988).
C. Domb and M. E. Fisher,Proc. Comb. Phil. Soc. 54:48 (1958).
I. Claes and C. Van den Broeck,J. Stat. Phys. 49:383 (1987).
E. H. Hauge,Phys. Fluids 13:1201 (1970).
Y. Okamura, E. Blaisten-Barojas, and S. Fujita,Phys. Rev. B 22:1638 (1980).
Author information
Authors and Affiliations
Additional information
This paper is dedicated to Nico van Kampen.
Rights and permissions
About this article
Cite this article
Ernst, M.H. Random walks with short memory. J Stat Phys 53, 191–201 (1988). https://doi.org/10.1007/BF01011552
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01011552