Random geometric subdivisions. Issue 1 (1st August 2012)

• Record Type: Journal Article
• Authors: Volkov, Stanislav
• Is Part Of: Random structures & algorithms. Volume 43:Issue 1(2013)
• Page Start: 115
• Page End: 130
• Publication Date: 2012-08-01
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20454
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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</p> </abstract>