Critical probability and scaling functions of bond percolation on two-dimensional random lattices

1998 ◽  
Vol 31 (15) ◽  
pp. 3429-3438 ◽  
Author(s):  
Ming-Chang Huang ◽  
Hsiao-Ping Hsu
Keyword(s):  
Scaling Functions ◽  
Bond Percolation ◽  
Two Dimensional ◽  
Critical Probability ◽  
Random Lattices

Bond percolation on two-dimensional random lattices

1997 ◽  
Vol 56 (17) ◽  
pp. 10743-10746 ◽  
Author(s):  
H. P. Hsu ◽  
M. C. Huang ◽  
K. J. Ling
Keyword(s):  
Bond Percolation ◽  
Two Dimensional ◽  
Random Lattices

Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
M. I. González-Flores ◽  
A. A. Torres ◽  
W. Lebrecht ◽  
A. J. Ramirez-Pastor
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Bond Percolation ◽  
Two Dimensional

Percolation on Penrose Tilings

1998 ◽  
Vol 41 (2) ◽  
pp. 166-177 ◽  
Author(s):  
A. Hof
Keyword(s):  
Large Class ◽  
Arbitrary Dimension ◽  
Bond Percolation ◽  
Critical Probability ◽  
Site Percolation ◽  
Aperiodic Tilings ◽  
Infinite Clusters ◽  
Almost All ◽  
Percolation Processes ◽  
Penrose Tilings

AbstractIn Bernoulli site percolation on Penrose tilings there are two natural definitions of the critical probability. This paper shows that they are equal on almost all Penrose tilings. It also shows that for almost all Penrose tilings the number of infinite clusters is almost surely 0 or 1. The results generalize to percolation on a large class of aperiodic tilings in arbitrary dimension, to percolation on ergodic subgraphs of ℤd, and to other percolation processes, including Bernoulli bond percolation.

On the time constant and path length of first-passage percolation

1980 ◽  
Vol 12 (04) ◽  
pp. 848-863 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Distribution Function ◽  
Time Constant ◽  
Path Length ◽  
Passage Time ◽  
Square Lattice ◽  
Bond Percolation ◽  
First Passage Percolation ◽  
Critical Probability ◽  
First Passage ◽  
Individual Bond

Let U be the distribution function of the passage time of an individual bond of the square lattice, and let pT be the critical probability above which the expected size of the open component of the origin (in the usual bond percolation) is infinite. It is shown that if (∗)U(0–) = 0, U(0) < pT , then there exist constants 0 < a, C 1 < ∞ such that a self-avoiding path of at least n steps starting at the origin and with passage time ≦ an} ≦ 2 exp (–C 1 n). From this it follows that under (∗) the time constant μ (U) of first-passage percolation is strictly positive and that for each c > 0 lim sup (1/n)Nn (c) <∞, where Nn (c) is the maximal number of steps in the paths starting at the origin with passage time at most cn.

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