= Uniqueness of the infinite percolation cluster
= Burton-Keane theorem
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{synonym}
For independent <site percolation> or <bond percolation> on the <cubic lattice> $\mathbb Z^d$, there is <almost surely> at most one <infinite percolation cluster> at every fixed parameter. Above the <percolation critical probability>, there is exactly one <almost surely>. This theorem is called the <Burton-Keane theorem>. Existence uses translation ergodicity together with positive <percolation probability>; uniqueness is a separate conclusion. At $p=1$ uniqueness is deterministic.
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