  We derive sub-Gaussian bounds for the annealed transition density of the
simple random walk on a high-dimensional loop-erased random walk. The walk
dimension that appears in these is the exponent governing the space-time
scaling of the process with respect to the extrinsic Euclidean distance, which
contrasts with the exponent given by the intrinsic graph distance that appears
in the corresponding quenched bounds. We prove our main result using novel
pointwise Gaussian estimates on the distribution of the high-dimensional
loop-erased random walk.
