Random geometric subdivisions

Details Random geometric subdivisions Random geometric subdivisions

2011-12-05

arxiv.org/abs/1112.0932v1

Mathematics

Probability

Scientific paper

We study several models of random geometric subdivisions arising from the model of Diaconis and Miclo (2011). In particular, we show that the limiting shape of an indefinite subdivision of a quadrilateral is a.s.\ a parallelogram. We also show that the geometric subdivisions of a triangle by angle bisectors converge (only weakly) to a non-atomic distribution, and that the geometric subdivisions of a triangle by choosing random points on its sides converges to a "flat" triangle, similarly to the result of Diaconis and Miclo (2011).

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