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Random geometric subdivisions

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

Abstract

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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