Excited Random Walk against a Wall

@inproceedings{Benjamini2005ExcitedRW,
  title={Excited Random Walk against a Wall},
  author={Itai Benjamini and Gady Kozma},
  year={2005}
}
We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of √ log n