Question

When does a finite size random graph percolate?

Answer 1

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.

Answer 2

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✔️✔️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

makes it clear that there is a strong link to percolation.

However ..... in bond percolation. The susceptibility p → χ(p) is the expected cluster size.


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