Brownian Motion on Compact Manifolds : Cover Time And

  title={Brownian Motion on Compact Manifolds : Cover Time And},
  author={LATE and POINTSAMIR and Dembo},
  • Published 2002
Let M be a smooth, compact, connected Riemannian manifold of dimension d ≥ 3 and without boundary. Denote by T (x, 2) the hitting time of the ball of radius 2 centered at x by Brownian motion on M . Then, C2(M) = supx∈M T (x, 2) is the time it takes Brownian motion to come within r of all points in M . We prove that C2(M)/2| log 2| → γdV (M) almost surely as 2→ 0, where V (M) is the Riemannian volume of M . We also obtain the “multi-fractal spectrum” f(α) for “late points”, i.e., the dimension… CONTINUE READING

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