Jante's law process

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2 Citations (SciVal)

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.
Original languageEnglish
Pages (from-to)414-439
JournalAdvances in Applied Probability
Volume50
Issue number2
DOIs
Publication statusPublished - 2018 Jun

Subject classification (UKÄ)

  • Mathematics
  • Probability Theory and Statistics

Keywords

  • Probability theory
  • Markov processes

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