  The growth exponent $\alpha$ for loop-erased or Laplacian random walk on the
integer lattice is defined by saying that the expected time to reach the sphere
of radius $n$ is of order $n^\alpha$. We prove that in two dimensions, the
growth exponent is strictly greater than one. The proof uses a known estimate
on the third moment of the escape probability and an improvement on the
discrete Beurling projection theorem.
