Abstract
The Green’s function of a random walk on a lattice is defined as the inverse of the operatorK-z1, whereK is the matrix of transition rates and z is an arbitrary complex parameter. The Green’s function for a symmetrical random walk in one dimension is here explicitly given in closed form for reflecting, periodic, and absorbing boundaries, and also for an infinite lattice.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Weiss, G. H. and Rubin, R. J. (1983),Adv. Chem. Phys. v52 (I. Prigogine and S. A. Rice, eds.), John Wiley, NY, pp. 363–505.
Montroll, E. W. and Schlesinger, M. F. (1984),Non Equilibrium Phenomena II (Lebowitz, J. L. and Montroll, E. W., eds.), Elsevier, Amsterdam, pp. 1–121.
Charles Darwin: His Life told in an autobiographical Chapter, and a selected series of his published letters (1896) (Darwin, F., ed.), D. Appleton, NY., p. 60.
Khantha, M. and Balakrishnan, V. (1983),Pranãna 21, p. 111.
Margenau, H. and Murphy, G. (1943),The Mathematics of Physics and Chemistry, Van Nostrand, NY, p. 523.
Mazo, R. M. and Van den Broeck, C. (1986),Phys. Rev. A34 2364.
Mazo, R. M. and Van den Broeck, C. (1987),J. Chem. Phys.,86, 454.
Weiss, G. H. (1967),Adv. Chem. Phys. v3 (I. Prigogine, ed.), John Wiley, NY, p. 3et seq.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mazo, R.M. On the Green’s function for a one-dimensional random walk. Cell Biophysics 11, 19–24 (1987). https://doi.org/10.1007/BF02797109
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02797109