Introduction to Bernoulli percolation

2 Everyone’s toolbox 4 2.1 Increasing coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Harris-FKG inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The van den Berg Kesten and the Reimer inequalities . . . . . . . . . . . . . . . . . 7 2.4 Margulis-Russo formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Ergodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

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