%0 Journal Article %1 Brummelhuis1992How %A Brummelhuis, M. %A Hilhorst, H. %D 1992 %J Physica A: Statistical Mechanics and its Applications %K lattice\_gas, random\_walks percolation coverage lattice-models finite-size diffusion critical-points %N 1-4 %P 35--44 %R 10.1016/0378-4371(92)90435-s %T How a random walk covers a finite lattice %U http://dx.doi.org/10.1016/0378-4371(92)90435-s %V 185 %X A random walker is confined to a finite periodic d -dimensional lattice of N initially white sites. When visited by the walk a site is colored black. After t steps of the walk, for t scaled appropriately with N , we determined the structure of the set of white sites. The variance of their number has a line of critical points in the td plane, which separates a mean-field region from a region with enhanced fluctuations. At d = 2 the critical point becomes a critical interval. Moreover, for d = 2 the set of white sites is fractal with a fractal dimensionality whose t -dependence we determine.

@article{Brummelhuis1992How, abstract = {{A random walker is confined to a finite periodic d -dimensional lattice of N initially white sites. When visited by the walk a site is colored black. After t steps of the walk, for t scaled appropriately with N , we determined the structure of the set of white sites. The variance of their number has a line of critical points in the td plane, which separates a mean-field region from a region with enhanced fluctuations. At d = 2 the critical point becomes a critical interval. Moreover, for d = 2 the set of white sites is fractal with a fractal dimensionality whose t -dependence we determine.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Brummelhuis, M. and Hilhorst, H.}, biburl = {https://www.bibsonomy.org/bibtex/2419d64900da514bd2b11837c5c7c540c/nonancourt}, citeulike-article-id = {4199145}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/0378-4371(92)90435-s}, day = 15, doi = {10.1016/0378-4371(92)90435-s}, interhash = {db410dcbacaa5b7afaab5a1ed386ebfc}, intrahash = {419d64900da514bd2b11837c5c7c540c}, issn = {03784371}, journal = {Physica A: Statistical Mechanics and its Applications}, keywords = {lattice\_gas, random\_walks percolation coverage lattice-models finite-size diffusion critical-points}, month = jun, number = {1-4}, pages = {35--44}, posted-at = {2009-03-20 15:57:37}, priority = {2}, timestamp = {2019-08-23T10:59:34.000+0200}, title = {{How a random walk covers a finite lattice}}, url = {http://dx.doi.org/10.1016/0378-4371(92)90435-s}, volume = 185, year = 1992 }