First, I give a simple but tricky proof that the Loewner driving process of the near-critical SLE(6) curve is a sub-martingale. Then I explain a conjectural exact form of this driving process. This is from joint work with Christophe Garban and Oded Schramm. Then, using a very different method, I will prove that the probability of having a left-right crossing in a square in \lambda-near-critical percolation, as \lambda\to-\infty, is about \exp(-|\lambda|^{4/3}).
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