Abstract: In this Friday lecture, I will present a very beautiful proof. I think this is more important than what this proof actually shows. But in case you are curious: Consider the integer grid on Z^2 and select every edge with probability p. What is the probability that the resulting graph has an infinite connected component? The classical Harris-Kesten Theorem states that this probability is 0 if p is at most 0.5, and 1 if it is bigger. Thus, something magic happens at p=0.5. A couple of years ago, Bollobas and Riordan gave a new and very elegant proof of this fact. What I like about it in particular, and why I present it at a Friday lecture, is that, although non-trivial, one can present it using mostly pictures and only few mathematical symbols. If you are even more curious: The question is motivated by statistical physics, for example by studying how water trickles through a porous rock.

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