Adatoms moving along the substrate surface under an STM tip cause a ra
ndom time dependence of the current, J(t). We have obtained simple exp
ressions for the average current [J(t)] and the temporary current corr
elation function [J(t + tau)J(tau)]tau - [J(t)]2 through the diffusion
coefficients of the adatoms and a few parameters of the tunneling gap
. The results offer a way to study the local diffusion of adatoms by t
reatment of experimentally measured J(t) dependencies.