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Title:
Critical lattice interfaces: polynomial rate of convergence to SLE curves
Speaker:
Abstract:
We discuss the rate of convergence of the critical interfaces of various critical lattice models to SLE. In particular, we examine the exploration process for critical percolation. We talk about the fact that for any "reasonable" critical percolation model for which the convergence of the exploration process is established, the polynomial rate of convergence must automatically hold. So far, the result is unconditional for the critical site percolation on the hexagonal lattice and for some of its generalizations, which will be discussed at the talk. We also analyze a general framework for establishing these types of results for other models, such as Harmonic Explorer and the Ising model. The talk is based on joint projects with L. Chayes, H. Lei, and L. Richards.
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