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Percolation for the Gaussian free field on the cable system

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Among percolation models with long-range correlations, the Gaussian free field on discrete graphs has received a lot of attention over the last few years, but not so much on its continuous equivalent, the cable system. I will present a brief history of the question, and explain why, for this model, the critical parameter is surprisingly equal to 0, and is thus explicitly known, on a large class of graphs

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