Talk:Percolation theory

percolation theory at industry
Im casually trying to figure oil oil moving through minerals as part of petroleum geology I would really appreciate actual industrial application descriptions with math that give an idea of the application of percolation theory to applied movement or diffusion. it would make the article more fun as well. also readers would possibly find an explanation of something like a fluid is passing through a stochastically channelized material, with a fractal number, yet all the channels are three times longer than they are wide, this has a particular kind of effect on transverse as well as flowdirection fluid motion a kind of "oh yeah, I see what they mean" opportunity

I appreciate that there are lots of nonlinearities n things, yet even a casual mention of something like "a repeating cube of fractally porous material within 3 radiaii of an open area twice as large has a particular flow rate" would be nifty. I know its wikipedia, so, like if I want a graph, maybe I should go make a graph then place it at the article, yet im hoping a person with casual applications material could describe a few things

What is
What is Bernoulli percolation theory?

p = 51?
Are you sure? I think probabilities should lie between 0 and 1. --202.40.139.171 05:45, 6 June 2007 (UTC)

Most likely it means p=51% (i.e. p=.51) 128.95.224.52 00:09, 19 October 2007 (UTC)

Bernoulli percolation vs. percolation theory
Bernoulli bond (resp. site) percolation is simply a more descriptive name for the percolation process that's described in the bulk of this article: every edge (resp. vertex) in the lattice is independently assigned a Bernoulli random variable with parameter $$p$$ (with $$0 \le p\le 1$$), where 1s represent open edges (or sites) and 0s represent closed edges (or sites). (Hence this percolation process is a Bernoulli process.)

It seems to me that the overall organization of the percolation-related articles (e.g. percolation, percolation theory, percolation threshold, 2D percolation cluster, directed percolation) is somewhat confusing due to lack of coordination. I think "percolation theory" usually refers to standard Bernoulli percolation, although as pointed out in the section "The different models," there are other related models that are more general or approach the idea of percolation from a different perspective. However, I'm not aware of any reference that describes this more general concept of "percolation theory" in a unified way, so I don't know if it would make sense to have an article describing generalized percolation theory separate from Bernoulli percolation. 128.95.224.52 00:06, 19 October 2007 (UTC)

Uses of the Theory in Science
ScienceDirect.com just published a report that uses percolation theory to explain locust swarms  A good summary is listed on ScienceDaily.com Do we want to include this in the article? In Popular Culture? Gregpennings (talk) 20:24, 30 December 2008 (UTC)

Hypercube in 3d?
This article refers to the hypercube (or hypercubic lattice) in 3d. What is meant by this? I would assume that a hypercubic lattice would be a cubic lattice in higher dimensions. —Preceding unsigned comment added by 129.215.104.124 (talk) 17:49, 27 July 2010 (UTC)

Dependent Percolation
I think there should be a whole section about dependent percolation on a general graph G=(N,E), i.e., an arbitrary probability measure on {0,1}^N. The content could be a list of questions and their answers if they exist. For example:

Natural questions:

1) What are examples for dependent percolation?

1) Under what assumptions does an infinite open cluster exist?

2)a) Under what assumptions can an infinite open cluster and an infinite closed cluster coexist? ...

2)b) Under what assumptions can we preclude the coexistence of an infinite open and an infinite closed cluster? ...

3) What do we know about the distribution of the cluster size? ...

etc.

Answers:

1) Ising-model, widom-rowlinson lattice model, etc.

2)see Liggett, T., Schonman, R.H., and Stacey, A.M. (1997)Domination by product measures, Ann, Probab. \textbf{25}, 71-96.

etc. — Preceding unsigned comment added by 138.246.2.177 (talk) 12:41, 2 July 2012 (UTC)

Is there really "no percolation in the critical phase" ?
"In dimension 2, the first fact ("no percolation in the critical phase") is proved for many lattices, using duality." Where are the sources of this statement? I found sources which stating the oppsite...for example look here: Langlands, R. Po, et al. "On the universality of crossing probabilities in two-dimensional percolation." Journal of statistical physics 67.3-4 (1992): 553-574. ( pdf at: http://publications.ias.edu/sites/default/files/universality-ps.pdf ) — Preceding unsigned comment added by 83.171.162.168 (talk) 15:55, 17 March 2014 (UTC)
 * I couldn't find where in that article the opposite is stated. If someone finds it, please record here where, so that the issue can be resolved. Geoffrey Grimmett (who wrote Percolation and seems to be something of an authority on the subject) gives a proof that there is no infinite cluster at the critical point on p. 224 of these notes. Joriki (talk) 17:10, 16 May 2020 (UTC)

Citing
You are doing it wrong. — Preceding unsigned comment added by 195.176.101.170 (talk) 12:56, 15 January 2016 (UTC)
 * See Parenthetical referencing. It's a valid citation style for Wikipedia, despite being less commonly used than footnotes. —David Eppstein (talk) 16:59, 15 January 2016 (UTC)

Is it too much trouble to say what you mean?
The section Subcritical and supercritical begins as follows:

"The main fact in the subcritical phase is "exponential decay". That is, when $p < p_{c}$, the probability that a specific point (for example, the origin) is contained in an open cluster (meaning a maximal connected set of "open" edges of the graph) of size $r$ decays to zero exponentially in $r$. This was proved for percolation in three and more dimensions by and independently by . In two dimensions, it formed part of Kesten's proof that $p_{c} = 1⁄2$."

But since percolation can be node percolation or edge percolation, and since the results depend on which network is under consideration (not just which dimension): The writer has not taken the trouble to tell the reader what is being talked about. This makes this passage of no use to the reader.50.205.142.50 (talk) 21:21, 14 May 2020 (UTC)