Percolation theory describes the behavior of connected clusters in a random graph.
Percolation theory describes the behavior of connected clusters in a random graph.
Questions tagged [percolation]
137 questions
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percolation - number of cycles around the origin
I try to study Percolation Theory by "A mini course on percolation theory" of Jeffrey E. Steif.
I am very curios about Exercise 2.4.
Show that the number of cycles around the origin of length n is at most $n4(3^{n−1})$.
I need to this on lattice…
com
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Percolation and hopping, has it been described?
This ultimately relates to a physics question, but It wasn't getting any answers, on physics.stackexchange. As it crosses the boundaries of each subject I was advised to post it here:
Has a system where conducting sites can percolate by hopping…
AncientSwordRage
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Generalized percolation problem
Consider a simple site percolation problem on, for example, a 2D square lattice. Each vertex is randomly either there or not with some probability. If two neighbouring vertices are present, then the edge between them is there too. If any connected…
Matthew Matic
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Largest cluster sizes in sub-critical percolation
Consider a sub-critical site percolation problem on a square lattice with $N$ sites.
In the limit of large $N$, the (ensemble averaged) size $\mu$ of the largest cluster scales as (see here)
$$
\mu \sim s(p) \log N
$$
What is the dependence on…
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Probability on Graphs. Percolation.
I am studying the book Probability on Graphs by Grimett. Grimett tells us that $\mu_1 \leq_{st} \mu_2$ if and only if $\mu_1(f)\leq\mu_2(f)$ for all increasing functions $f:\Omega\to \mathbb{R}$. I want to proof this. I tried to use the standard…
user202723
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