Random Walks on Lattices. II Export

@article{citeulike:667579, abstract = {Formulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions. Generally this time is proportional to the number of lattice points.The number of distinct points visited after n steps on a k-dimensional lattice (with k 3) when n is large is a1n + a2n\½ + a3 + a4n\&\#150;\½ + . The constants a1 \&\#150; a4 have been obtained for walks on a simple cubic lattice when k = 3 and a1 and a2 are given for simple and face-centered cubic lattices. Formulas have also been obtained for the number of points visited r times in n steps as well as the average number of times a given point has been visited.The probability F(c) that a walker on a one-dimensional lattice returns to his starting point before being trapped on a lattice of trap concentration c is F(c) = 1 + [c/(1 \&\#150; c)] log c.Most of the results in this paper have been derived by the method of Green's functions. \©1965 The American Institute of Physics}, author = {Montroll, Elliott W. and Weiss, George H.}, citeulike-article-id = {667579}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000006000002000167000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aip.org/link/?JMP/6/167}, citeulike-linkout-2 = {http://dx.doi.org/10.1063/1.1704269}, doi = {10.1063/1.1704269}, journal = {Journal of Mathematical Physics}, keywords = {ctrw, diffusion, lattice\_model, random\_walks}, number = {2}, pages = {167--181}, posted-at = {2009-03-02 16:17:38}, priority = {2}, publisher = {AIP}, title = {Random Walks on Lattices. II}, url = {http://dx.doi.org/10.1063/1.1704269}, volume = {6}, year = {1965} }

TY - JOUR ID - citeulike:667579 L3 - citeulike-article-id:667579 N2 - Formulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions. Generally this time is proportional to the number of lattice points.The number of distinct points visited after n steps on a k-dimensional lattice (with k 3) when n is large is a1n + a2n½ + a3 + a4n–½ + . The constants a1 – a4 have been obtained for walks on a simple cubic lattice when k = 3 and a1 and a2 are given for simple and face-centered cubic lattices. Formulas have also been obtained for the number of points visited r times in n steps as well as the average number of times a given point has been visited.The probability F(c) that a walker on a one-dimensional lattice returns to his starting point before being trapped on a lattice of trap concentration c is F(c) = 1 + [c/(1 – c)] log c.Most of the results in this paper have been derived by the method of Green's functions. ©1965 The American Institute of Physics IS - 2 JF - Journal of Mathematical Physics EP - 181 TI - Random Walks on Lattices. II PB - AIP VL - 6 SP - 167 KW - ctrw KW - diffusion KW - lattice_model KW - random_walks AU - Montroll, Elliott AU - Weiss, George PY - 1965/// UR - http://dx.doi.org/10.1063/1.1704269 ER -