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On near-critical SLE(6) and on the tail in Cardy's formula

Presented by: 
G Pete [Hungarian Academy of Sciences & Technical University of Budapest]
Date: 
Friday 30th January 2015 - 13:30 to 14:30
Venue: 
INI Seminar Room 1
Abstract: 
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons