Student Probability Seminar

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SLE and Conformal Invariance

Speaker: Reza Gheissari

Location: Warren Weaver Hall 202

Date: Friday, October 31, 2014, 2 p.m.

Synopsis:

Motivated by the scaling limits of a wide range of statistical mechanics models including LERW, percolation, GFF and Ising model, Schramm in 2000 introduced Stochastic/Schramm Loewner Evolution (\(SLE_\kappa\)). We motivate and introduce chordal \(SLE_\kappa\) and some interesting properties of its dependence on parameter \(\kappa\). We then give flavors for the proofs of convergence of critical percolation and Ising interfaces to \(SLE_\kappa\) due to Smirnov (2010).