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Jante's law process

Published online by Cambridge University Press:  26 July 2018

Philip Kennerberg
Affiliation:
Lund University
Stanislav Volkov
Affiliation:
Lund University
Corresponding

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.

Type
Original Article
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. CrossRefGoogle Scholar
[2]Grinfeld, M., Volkov, S. and Wade, A. R. (2015). Convergence in a multidimensional randomized Keynesian beauty contest. Adv. Appl. Prob. 47, 5782. CrossRefGoogle Scholar
[3]Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 1330. CrossRefGoogle 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

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