2011/12/05 by Stanislav Volkov, Volkov, Stanislav
Engineering · Mathematics · #60D05 #60J05 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1112.0932
openalex publication_date 2011/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).