Abstract: In this talk, we introduce the stationary harmonic measure in the upper half plane. By controlling

the bounds of this measure, we are able to define a continuous diffusion limit aggregation (DLA) in the

upper half plane with absorbing boundary conditions. We prove that the growth rate of the longest arm in

the DLA with respect to time $t$ is no more than $o(t^{2+\epsilon})$. We also show that the stationary

harmonic measure of an infinite set in the upper planar lattice can be represented as the proper scaling

limit of the classical harmonic measure of truncations of the infinite set.