HOW A RANDOM-WALK COVERS A FINITE LATTICE

被引:19
作者
BRUMMELHUIS, MJAM [1 ]
HILHORST, HJ [1 ]
机构
[1] UNIV PARIS 11,CNRS,PHYS THEOR & HAUTES ENERGIES LAB,F-91405 ORSAY,FRANCE
来源
PHYSICA A | 1992年 / 185卷 / 1-4期
关键词
D O I
10.1016/0378-4371(92)90435-S
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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 determine 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.
引用
收藏
页码:35 / 44
页数:10
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