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Self-avoiding walk ensembles that should converge to SLE

Mathematical Physics & Probability

Speaker: Tom Kennedy, University of Arizona
Location: 3106 MSB
Start time: Wed, May 9 2012, 5:10PM

The self-avoiding walk is a model of random walks on a lattice in which one only allows walks which do not intersect themselves. It is believed that in two dimensions this model should be conformally invariant, and the scaling limit should be the Schramm-Loewner evolution (SLE) with kappa=8/3. There are a variety of different ensembles of self-avoiding walks that should converge to SLE in the scaling limit. I will review some of the well known conjectures and present some new ones. There are no proofs of any of these conjectures, but most of them are supported by Monte Carlo simulations.