Conditioning SLEs and loop erased random walks
Michel Bauer (IPHT, LPTENS), Denis Bernard (LPTENS), Tom Kennedy
TL;DR
This paper studies the properties of dipolar SLE(k), especially for k=2, revealing a unique characterization related to conditioning and providing a new probability calculation for SLE(2).
Contribution
It identifies a unique property of dipolar SLE(2) related to conditioning, and computes a new bulk passage probability for this case.
Findings
k=2 is uniquely characterized by its conditioning property
Derived a new bulk passage probability for SLE(2)
Showed that conditioned dipolar SLE(2) coincides with unconditioned on an interval
Abstract
We discuss properties of dipolar SLE(k) under conditioning. We show that k=2, which describes continuum limits of loop erased random walks, is characterized as being the only value of k such that dipolar SLE conditioned to stop on an interval coincides with dipolar SLE on that interval. We illustrate this property by computing a new bulk passage probability for SLE(2).
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