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Boundary Measures and Natural Time Parameterization for SLE

Date: 
Thursday 18th June 2015 - 16:30 to 17:30
Venue: 
INI Seminar Room 1
Abstract: 
Among Greg's many important contributions to the Schramm-Loewner evolution, he and his co-authors have in recent years been largely responsible for the construction and analysis of the natural time parameterization. The term ``natural'' refers to the parameterization favored by probabilists in the discrete curve setting, one unit of time per lattice site, and although it has not yet been shown that this discrete time parameterization converges it is still possible to define and study what should be the corresponding time parameterization for the continuum SLE curve. I will review many of the results in this direction that are due to Greg et al, along with some related results of my own in the boundary case, and then discuss some work in progress for extending the results on the boundary.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons