Distribution of poles in a series expansion of the asymmetric directed-bond percolation probability on the square lattice

1998 ◽  
Vol 31 (48) ◽  
pp. 9613-9620 ◽  
Author(s):  
Norio Inui
Keyword(s):  
Series Expansion ◽  
Square Lattice ◽  
Bond Percolation ◽  
Distribution Of Poles ◽  
Percolation Probability

On spàtial general epidemics and bond percolation processes

1984 ◽  
Vol 21 (4) ◽  
pp. 911-914 ◽  
Author(s):  
Kari Kuulasmaa ◽  
Stan Zachary
Keyword(s):  
Lower Bound ◽  
Bond Percolation ◽  
Percolation Process ◽  
Percolation Probability ◽  
Percolation Processes

We show that a lower bound for the probability that a spatial general epidemic never becomes extinct is given by the percolation probability of an associated bond percolation process.

Exact site-percolation probability on the square lattice

2021 ◽  
Author(s):  
Stephan Mertens
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Percolation Threshold ◽  
Percolation Cluster ◽  
Square Lattice ◽  
Site Percolation ◽  
Exact Probability ◽  
Percolation Probability ◽  
A Site ◽  
Time And Space Complexity

Abstract We present an algorithm to compute the exact probability $R_{n}(p)$ for a site percolation cluster to span an $n\times n$ square lattice at occupancy $p$. The algorithm has time and space complexity $O(\lambda^n)$ with $\lambda \approx 2.6$. It allows us to compute $R_{n}(p)$ up to $n=24$. We use the data to compute estimates for the percolation threshold $p_c$ that are several orders of magnitude more precise than estimates based on Monte-Carlo simulations.

On spàtial general epidemics and bond percolation processes

1984 ◽  
Vol 21 (04) ◽  
pp. 911-914 ◽  
Author(s):  
Kari Kuulasmaa ◽  
Stan Zachary
Keyword(s):  
Lower Bound ◽  
Bond Percolation ◽  
Percolation Process ◽  
Percolation Probability ◽  
Percolation Processes

We show that a lower bound for the probability that a spatial general epidemic never becomes extinct is given by the percolation probability of an associated bond percolation process.

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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