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On Lundh's percolation diffusion
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A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.
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CARROLL, Tom, O'DONOVAN, Julie and ORTEGA CERDÀ, Joaquim. On Lundh's percolation diffusion. Stochastic Processes and their Applications. 2012. Vol. 122, num. 4, pags. 1988-1997. ISSN 0304-4149. [consulted: 26 of June of 2026]. Available at: https://hdl.handle.net/2445/34315