Nontrivial Phase Transition in a Continuum Mirror Model

Matthew Harris ()
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Matthew Harris: Delft University of Technology

Journal of Theoretical Probability, 2001, vol. 14, issue 2, 299-317

Abstract: Abstract We consider a Poisson point process on $$\mathbb{R}^2$$ with intensity λ, and at each Poisson point we place a two sided mirror of random length and orientation. The length and orientation of a mirror is taken from a fixed distribution, and is independent of the lengths and orientations of the other mirrors. We ask if light shone from the origin will remain in a bounded region. We find that there exists a $$\lambda _H^ *$$ with 0 $$\lambda _H^*$$ , light from the origin will almost surely remain in a bounded region.

Keywords: percolation; wind tree model; Lorenz model; phase transition (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1011185511572

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