Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,853 answers , 20,624 comments
1,470 users with positive rep
501 active unimported users
More ...

When does a finite size random graph percolate?

+ 4 like - 0 dislike
42 views

Assume we are simulating percolation on a 2d lattice. While the system is of finite size, we say that the critical state appears when a cluster connects two opposing ends of the lattice. The bigger the lattice the better our approximation.

My question is: assume we are doing the same thing but instead of a lattice we have a random graph with a known degree distribution. As we are increasing the occupation probability, who do we know that we reached percolation?

In other words, how does the 'connecting opposing ends' assumption translate to random graph topologies?


This post imported from StackExchange Physics at 2016-11-13 12:37 (UTC), posted by SE-user Dionysios Gerogiadis

asked Nov 10, 2016 in Computational Physics by Dionysios Gerogiadis (25 points) [ revision history ]
edited Nov 13, 2016 by Dilaton
This question is actually about mathematics. Anyway here and here and here you could find something useful.

This post imported from StackExchange Physics at 2016-11-13 12:37 (UTC), posted by SE-user valerio92
As a far younger member and a non-physicist accept your remark, nonetheless I am surprised. Percolation in random networks is an active field of researcher with numerous publications in Physics journals. The works of Callaway, Newman, Gleeson, Watts and others focus on similar stuff. That is why I posted here.

This post imported from StackExchange Physics at 2016-11-13 12:37 (UTC), posted by SE-user Dionysios Gerogiadis

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar\varnothing$sicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...