2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76683The growth exponent $α$ 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 $n^α$. 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.Probability60J15text