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An easier extra head scheme for the Poisson process on $\mathbf{R}^{n}$

Author(s): Robert Service
Journal: Proc. Amer. Math. Soc. 138 (2010), 3703-3705.
MSC (2010): Primary 60G55, 60G10
Posted: May 21, 2010
MathSciNet review: 2661568
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Abstract | References | Similar articles | Additional information

Abstract: A simple construction is presented whereby a nonrandomized extra head scheme for stationary ergodic point processes on the line due to T. Liggett (2002) is lifted to $\mathbf{R}^{n}$ in the Poisson case. This gives the simplest construction for a nonrandomized extra head scheme in higher dimensions, yet the method has been overlooked in previous work on the subject.

References:

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2.: C. Hoffman, A. Holroyd, Y. Peres, A stable marriage of Poisson and Lebesgue, Ann. Probab. (4), 34 (2006), 1241-1272. MR 2257646 (2007k:60034)
3.: C. Hoffman, A. Holroyd, Y. Peres, Tail Bounds for the Stable Marriage of Poisson and Lebesgue, arXiv:math/0507324v1 (2005).
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5.: A. Holroyd, T. Liggett, How to find an extra head: Optimal random shifts of Bernoulli and Poisson random fields, Ann. Probab. 29 (2001), 1405-1425. MR 1880225 (2003a:60075)
6.: O. Kallenberg, Foundations of Modern Probability, Second Edition, Probability and Its Applications, Springer-Verlag, New York, 2002. MR 1876169 (2002m:60002)
7.: T. Liggett, Tagged particle distributions or how to choose a head at random, in In and out of equilibrium, Progr. Probab., 51, Birkhäuser Boston, Boston, MA, 2002. MR 1901951 (2003e:60110)
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Additional Information:

Robert Service
Affiliation: Department of Mathematics and Statistics, University of Helsinki, SF-00014 Helsinki, Finland
Email: robert.service@helsinki.fi

DOI: 10.1090/S0002-9939-2010-10427-6
PII: S 0002-9939(2010)10427-6
Keywords: Extra head, Poisson process, stochastic geometry
Received by editor(s): June 11, 2009
Received by editor(s) in revised form: January 28, 2010 and January 29, 2010
Posted: May 21, 2010
Communicated by: Richard C. Bradley
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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