Random geometric subdivisions

Stanislav Volkov

doi:10.1002/rsa.20454

Random geometric subdivisions

Stanislav Volkov

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

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

Original language	English
Pages (from-to)	115-130
Number of pages	16
Journal	Random Structures and Algorithms
Volume	43
Issue number	1
DOIs	https://doi.org/10.1002/rsa.20454
Publication status	Published - Aug 2013

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title = "Random geometric subdivisions",

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 ",

author = "Stanislav Volkov",

year = "2013",

month = aug,

doi = "10.1002/rsa.20454",

language = "English",

volume = "43",

pages = "115--130",

journal = "Random Structures and Algorithms",

issn = "1042-9832",

publisher = "John Wiley & Sons, Inc",

number = "1",

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T1 - Random geometric subdivisions

AU - Volkov, Stanislav

PY - 2013/8

Y1 - 2013/8

N2 - 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

AB - 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

U2 - 10.1002/rsa.20454

DO - 10.1002/rsa.20454

M3 - Article (Academic Journal)

SN - 1042-9832

VL - 43

SP - 115

EP - 130

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 1

ER -

Random geometric subdivisions

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