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Title:
On the continuity of SLE(\kappa) in \kappa and related results
Speaker:
Abstract:
SLE(\kappa) is a family of random fractal curves constructed by solving the Loewner equation with a standard Brownian motion times the square-root of \kappa as driving term. A natural question that has been asked is whether almost surely the SLE(\kappa) curves simultaneously exist and change continuously as the parameter \kappa is varied in an interval; there exist examples of deterministic Loewner chains with driving terms more regular than Brownian motion for which the corresponding statement is false. We will discuss a result giving a positive answer to this question and also indicate how these ideas combined with certain geometric estimates can be used to obtain power-law convergence rate results for, e.g., the loop-erased random walk path, when a rate for the driving term is known. The talk is in part based on joint work with Rohde and Wong
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