The Schramm-Loewner Evolution and the Gaussian Free Field

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• Dr Jason Miller, MIT
• Tuesday 06 November 2012, 15:00-16:00
• MR2.

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The Schramm-Loewner evolution (SLE) is the canonical model of a non-crossing conformally invariant random curve, introduced by Oded Schramm in 1999 as a candidate for the scaling limit of loop erased random walk and the interfaces in critical percolation. The development of SLE has been one of the most exciting areas in probability over the last decade because Schramm’s curves have now been rigorously shown to describe the limiting interfaces of a number of different two-dimensional models from statistical mechanics. Work on this topic has so far led to two Fields medals (Werner, 2006 and Smirnov, 2010). The first part of this talk will be a basic introduction to SLE . In the second part of the talk, I will describe the work of Sheffield, Schramm-Sheffield, and Dubédat on how SLEs are related to a certain random geometry which is generated by the GFF . Namely, SLE can be realized as the flow lines of the random vector field eih/x where h is a GFF and x > 0.

This talk is part of the Cambridge Centre for Analysis talks series.

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