Author

Patryk Morawski

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Preprint Aug 2026

The critical probability for percolation on finite graphs

We determine the critical probability for Bernoulli bond percolation on essentially any finite graph. Namely, letting $\lambda(G)$ denote the spectral radius (maximum eigenvalue) of $G$, we prove that the critical probability is at $1/\lambda(G)$: above this probability there is typically a component of order $\Omega(\...

Micha Christoph, Patryk Morawski, Yuval Wigderson · 1 citation