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Random geometric subdivisions

Volkov, Stanislav LU orcid (2013) In Random Structures & Algorithms 43(1). p.115-130
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).
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Barycentric subdivision, geometric probability, Markov chain, iterated random functions
in
Random Structures & Algorithms
volume
43
issue
1
pages
115 - 130
publisher
John Wiley & Sons Inc.
external identifiers
  • wos:000320729700005
  • scopus:84879502394
ISSN
1098-2418
DOI
10.1002/rsa.20454
language
English
LU publication?
yes
id
03eba868-d272-4362-98c1-11439516917c (old id 3241508)
date added to LUP
2016-04-01 10:27:56
date last changed
2022-01-25 23:31:48
@article{03eba868-d272-4362-98c1-11439516917c,
  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).}},
  author       = {{Volkov, Stanislav}},
  issn         = {{1098-2418}},
  keywords     = {{Barycentric subdivision; geometric probability; Markov chain; iterated random functions}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{115--130}},
  publisher    = {{John Wiley & Sons Inc.}},
  series       = {{Random Structures & Algorithms}},
  title        = {{Random geometric subdivisions}},
  url          = {{http://dx.doi.org/10.1002/rsa.20454}},
  doi          = {{10.1002/rsa.20454}},
  volume       = {{43}},
  year         = {{2013}},
}