The growth exponent for planar loop-erased random walk

Abstract

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.

62 pages, 7 figures; fixed typos, added references

References in corpus (2)

• Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
• Dimension and natural parametrization for SLE curves