Smirnov’s Theorem : dependence flowchart

This last semester we had a reading group on percolation theory, using the new book by Bollobas and Riordan. The crowning moment of our discussions was a 3-week trek through the proof of Smirnov’s theorem, which shows the conformal invariance of crossing probabilities for the triangular lattice. The book apparently contains the first “complete” proof in print. It’s quite involved, and for my part of the presentation I made the following flowchart of the structure of the proof:

Smirnov’s Theorem Flowchart


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