On Lundh’s percolation diffusion

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 spheri...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 122; no. 4; pp. 1988 - 1997
Main Authors Carroll, Tom, O’Donovan, Julie, Ortega-Cerdà, Joaquim
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2012
Subjects
Brownian motion
Markov processes
Percolation
Poisson point process
Potential theory (Mathematics)
Probabilitats
Probabilities
Processos de Markov
Teoria del potencial (Matemàtica)
60J65
Brownian motion
Percolation
Poisson point process
60K35
31B15
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2011.12.010