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Jante's law process

Part of: Markov processes Special processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  26 July 2018

Philip Kennerberg  and
Stanislav Volkov
Philip Kennerberg*
Affiliation:
Lund University
Stanislav Volkov*
Affiliation:
Lund University
*
* Postal address: Centre for Mathematical Sciences, Lund University, Box 118, SE-22100 Lund, Sweden.
* Postal address: Centre for Mathematical Sciences, Lund University, Box 118, SE-22100 Lund, Sweden.
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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.

Keywords

Keynesian beauty contestrank-driven processinteracting particle system

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces 60D05: Geometric probability and stochastic geometry
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 2 , June 2018 , pp. 414 - 439
Copyright
Copyright © Applied Probability Trust 2018 

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References

[1]Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular Variation (Encyclopedia Math. Appl. 27). Cambridge University Press. Google Scholar
[2]Grinfeld, M., Volkov, S. and Wade, A. R. (2015). Convergence in a multidimensional randomized Keynesian beauty contest. Adv. Appl. Prob. 47, 57–82. Google Scholar
[3]Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13–30. Google Scholar
[4]Parthasarathy, K. R. (2005). Probability Measures on Metric Spaces. AMS Chelsea Publishing, Providence, RI. Google Scholar
[5]Sandemose, A. (1936). A Fugitive Crosses His Tracks. Knopf, New York. Google Scholar