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Jante's law process

Kennerberg, Philip LU and Volkov, Stanislav LU orcid (2018) In Advances in Applied Probability 50(2). p.414-439
Abstract
Consider the process which starts with N ≥ 3 distinct points on ℝd, and fix a positive integer K < N. Of the total N points keep those N - K which minimize the energy amongst all the possible subsets of size N - K, and then replace the removed points by K independent and identically distributed points sampled according to some fixed distribution ζ. Repeat this process ad infinitum. We obtain various quite nonrestrictive conditions under which the set of points converges to a certain limit. This is a very substantial generalization of the `Keynesian beauty contest process' introduced in Grinfeld et al. (2015), where K = 1 and the distribution ζ was uniform on the unit cube.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Sannolikhetsteori, Stokastiska processer, Probability theory, Markov processes
in
Advances in Applied Probability
volume
50
issue
2
pages
414 - 439
publisher
Applied Probability Trust
external identifiers
  • scopus:85050694358
ISSN
0001-8678
DOI
10.1017/apr.2018.20
language
English
LU publication?
yes
id
1d098f1a-a703-44e4-8539-93780cc10567
date added to LUP
2018-03-16 16:22:32
date last changed
2021-09-15 05:23:20
@article{1d098f1a-a703-44e4-8539-93780cc10567,
  abstract     = {Consider the process which starts with N ≥ 3 distinct points on ℝd, and fix a positive integer K &lt; N. Of the total N points keep those N - K which minimize the energy amongst all the possible subsets of size N - K, and then replace the removed points by K independent and identically distributed points sampled according to some fixed distribution ζ. Repeat this process ad infinitum. We obtain various quite nonrestrictive conditions under which the set of points converges to a certain limit. This is a very substantial generalization of the `Keynesian beauty contest process' introduced in Grinfeld et al. (2015), where K = 1 and the distribution ζ was uniform on the unit cube.},
  author       = {Kennerberg, Philip and Volkov, Stanislav},
  issn         = {0001-8678},
  language     = {eng},
  number       = {2},
  pages        = {414--439},
  publisher    = {Applied Probability Trust},
  series       = {Advances in Applied Probability},
  title        = {Jante's law process},
  url          = {http://dx.doi.org/10.1017/apr.2018.20},
  doi          = {10.1017/apr.2018.20},
  volume       = {50},
  year         = {2018},
}