  We review some recently completed research that establishes the scaling limit
of Fomin's identity for loop-erased random walk on Z^2 in terms of the chordal
Schramm-Loewner evolution (SLE) with parameter 2. In the case of two paths, we
provide a simplified proof of the identity for loop-erased random walk and
simple random walk, and prove directly that the corresponding identity holds
for chordal SLE(2) and Brownian motion. We also include a brief introduction to
SLE and discussion of the relationship between SLE(2) and loop-erased random
walk.
