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A note on disjoint-occurrence inequalities for marked Poisson point processes

Part of: Distribution theory - Probability Stochastic processes Special processes

Published online by Cambridge University Press:  14 July 2016

J. van den Berg
J. van den Berg*
Affiliation:
CWI
*
∗Postal address: CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands.
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Abstract

For (marked) Poisson point processes we give, for increasing events, a new proof of the analog of the BK inequality. In contrast to other proofs, which use weak-convergence arguments, our proof is ‘direct' and requires no extra topological conditions on the events. Apart from some well-known properties of Poisson point processes, the proof is self-contained.

Keywords

DISJOINT OCCURRENCECONTINUUM PERCOLATIONPOISSON POINT PROCESSES

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 60G55: Point processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 420 - 426
Copyright
Copyright © Applied Probability Trust 1996 

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