Translator Disclaimer
March 2015 Convergence in a multidimensional randomized Keynesian beauty contest
Michael Grinfeld, Stanislav Volkov, Andrew R. Wade
Author Affiliations +
Adv. in Appl. Probab. 47(1): 57-82 (March 2015). DOI: 10.1239/aap/1427814581

Abstract

We study the asymptotics of a Markovian system of N ≥ 3 particles in [0, 1]d in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent U[0, 1]d random particle. We show that the limiting configuration contains N - 1 coincident particles at a random location ξN ∈ [0, 1]d. A key tool in the analysis is a Lyapunov function based on the squared radius of gyration (sum of squared distances) of the points. For d = 1, we give additional results on the distribution of the limit ξN, showing, among other things, that it gives positive probability to any nonempty interval subset of [0, 1], and giving a reasonably explicit description in the smallest nontrivial case, N = 3.

Citation

Download Citation

Michael Grinfeld. Stanislav Volkov. Andrew R. Wade. "Convergence in a multidimensional randomized Keynesian beauty contest." Adv. in Appl. Probab. 47 (1) 57 - 82, March 2015. https://doi.org/10.1239/aap/1427814581

Information

Published: March 2015
First available in Project Euclid: 31 March 2015

zbMATH: 1318.60100
MathSciNet: MR3327315
Digital Object Identifier: 10.1239/aap/1427814581

Subjects:
Primary: 60J05
Secondary: 60D05, 60F15, 60K35, 82C22, 91A15

Rights: Copyright © 2015 Applied Probability Trust

JOURNAL ARTICLE
26 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 1 • March 2015
Back to Top