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Percolation: the bunkbed conjecture on the complete graph

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In the percolation model, we start with a predetermined graph, and flip a coin for every edge; if the coin lands heads, then the edge is kept, if tails, the edge if removed. The coin need not be fair, but the coin flips for different edges are independent. In percolation theory, one studies the resultant random graph. The model is simple to define and has been studied extensively. However, many statements about the random graph that seem very intuitive turn out to be hard to prove. We look at a special case of the Bunkbed Conjecture; this is precisely such a statement. The talk is based on joint work (arXiv:1803.07647) with Peter van Hintum.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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