On Stationary Harmonic Measure and Diffusion Limited Aggregation in the Upper Half Plane
报告人：Yuan Zhang (Peking University)
时间：2018-11-27 10:40-11:30
地点：Room 1304, Sciences Building No. 1
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.
