Conditioning SLEs and loop erased random walks
  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). 
Michel Bauer (IPHT, LPTENS), Denis Bernard (LPTENS), Tom Kennedy