Cover times for Brownian motion and random walks in two dimensions

@inproceedings{Dembo2005CoverTF,
  title={Cover times for Brownian motion and random walks in two dimensions},
  author={Amir Dembo and Yuval Peres and Jay Rosen and Ofer Zeitouni},
  year={2005}
}
Let T (x, ε) denote the first hitting time of the disc of radius ε centered at x for Brownian motion on the two dimensional torus T2. We prove that supx∈T2 T (x, ε)/| log ε|2 → 2/π as ε → 0. The same applies to Brownian motion on any smooth, compact connected, two-dimensional, Riemannian manifold with unit area and no boundary. As a consequence, we prove a… CONTINUE READING

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