SEARCH

SEARCH BY CITATION

Keywords:

  • barycentric subdivision;
  • geometric probability;
  • Markov chain;
  • iterated random functions

Abstract

We study several models of random geometric subdivisions arising from the model of Diaconis and Miclo (Combin Probab Comput 20 (2011) 213–237). 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 (Combin Probab Comput 20 (2011) 213–237). © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013