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When does a finite size random graph percolate?

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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

commented Nov 10, 2016 by valerio92 (10 points) [ no revision ]

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

commented Nov 10, 2016 by Dionysios Gerogiadis (25 points) [ no revision ]

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