CPL - Chalmers Publication Library

# Percolation Diffusion

Torbjörn Lundh (Institutionen för matematik)
Stochastic Processes and their Applications (0304-4149). Vol. 95 (2001), 2, p. 235-244.

Let a Brownian motion in the unit ball be absorbed if it hits a set generated by a radially symmetric Poisson point process. The point set is fattened by putting a ball with a constant hyperbolic radius on each point. When is the probability non-zero that the Brownian motion hits the boundary of the unit ball? That is, manage to avoid all the Poisson balls and percolate diffusively all the way to the boundary. We will show that if the bounded Poisson intensity at a point z is ν(d(0,z)), where d(· ,·) is the hyperbolic metric, then the Brownian motion percolates diffusively if and only if $\nu \in L^1$.

Nyckelord: Percolation, Brownian motion, Poisson process, hyperbolicgeometry, minimal thinness

CPL Pubid: 23854

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# Institutioner (Chalmers)

Institutionen för matematik (1987-2001)