We give a new proof of a result of Kenyon that the growth exponent for loop-erased random walks in two dimensions is 5/4. The proof uses the convergence of LERW to Schramm-Loewner evolution with parameter 2, and is valid for irreducible bounded symmetric random walks on any two dimensional discrete lattice.
"The growth exponent for planar loop-erased random walk." Electron. J. Probab. 14 1012 - 1073, 2009. https://doi.org/10.1214/EJP.v14-651