Random geometric subdivisions
(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:
https://lup.lub.lu.se/record/3241508
- author
- Volkov, Stanislav LU
- organization
- publishing date
- 2013
- 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}}, }