"Percolation clusters as generators for orientation ordering",
(with Roy, R.)
Journal of statistical physics
Volume 168, January 2017, Pages 1259-1275
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Needles at different orientations are placed in an i.i.d. manner at points of a Poisson point process on R2 of density . Needles at the same direction have the same length, while needles at different directions maybe of different lengths. We study the geometry of a finite cluster when needles have only two possible orientations and when needles have only three possible orientations. In both these cases the asymptotic shape of the finite cluster as Ɂ is shown to consists of needles only in two directions. In the two orientations case the shape does not depend on the orientation but just on the i.i.d. structure of the orientations, while in the three orientations case the shape depend on all the parameters, i.e. the i.i.d. structure of the orientations, the lengths and the orientations of the needles.
