Abstract for the talk at 04.02.2014 (15:15 h)Oberseminar ANALYSIS - PROBABILITY
Vincent Beffara (ENS Lyon, France)
Percolation on mesoscopic lattices
In a celebrated paper, Smirnov proved that critical site-percolation on the regular triangular lattice has a non-trivial, conformally invariant scaling limit and that this can be used to derive for instance the value of critical exponents. The argument is unfortunately very speciﬁc to this particular lattice, and so far has not been generalized to any other natural case in particular, percolation on ℤ2 is much beyond reach of current methods. I will present one direction in which the proof can be extended into a non-trivial class of models that somehow interpolate between the triangular lattice and general planar cases.