The incipient infinite cluster in two-dimensional percolation

1986 ◽  
Vol 73 (3) ◽  
pp. 369-394 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Two Dimensional ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster

scholarly journals Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions

2008 ◽  
Vol 278 (2) ◽  
pp. 385-431 ◽  
Author(s):  
Martin T. Barlow ◽  
Antal A. Járai ◽  
Takashi Kumagai ◽  
Gordon Slade
Keyword(s):  
Random Walk ◽  
Oriented Percolation ◽  
High Dimensions ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster

PERCOLATION PROPERTIES AND UNIVERSALITY CLASS OF A MULTIFRACTAL RANDOM TILING

2005 ◽  
Vol 16 (02) ◽  
pp. 317-325 ◽  
Author(s):  
M. G. PEREIRA ◽  
G. CORSO ◽  
L. S. LUCENA ◽  
J. E. FREITAS
Keyword(s):  
Critical Phenomenon ◽  
Universality Class ◽  
Scaling Exponent ◽  
Two Dimensional ◽  
Regular Lattice ◽  
Local Anisotropy ◽  
Infinite Cluster ◽  
A Value ◽  
Random Tiling ◽  
Correlated Percolation

We study percolation as a critical phenomenon on a random multifractal support. The scaling exponent β related to the mass of the infinite cluster and the fractal dimension of the percolating cluster df are quantities that have the same value as the ones from the standard two-dimensional regular lattice percolation. The scaling exponent ν related to the correlation length is sensitive to the local anisotropy and assumes a value different from standard percolation. We compare our results with those obtained from the percolation on a deterministic multifractal support. The analysis of ν indicates that the deterministic multifractal is more anisotropic than the random multifractal. We also analyze connections with correlated percolation problems and discuss some possible applications.

scholarly journals Random walk on the incipient infinite cluster on trees

2006 ◽  
Vol 50 (1-4) ◽  
pp. 33-65 ◽  
Author(s):  
Martin T. Barlow ◽  
Takashi Kumagai
Keyword(s):  
Random Walk ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster
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