Conditional percolation on one-dimensional lattices

Conditional percolation on one-dimensional lattices

Marina Axelson-Fisk and Olle Häggström

Source: Adv. in Appl. Probab. Volume 41, Number 4 (2009), 1102-1122.

Abstract

Conditioning independent and identically distributed bond percolation with retention parameter p on a one-dimensional periodic lattice on the event of having a bi-infinite path from -∞ to ∞ is shown to make sense, and the resulting model exhibits a Markovian structure that facilitates its analysis. Stochastic monotonicity in p turns out to fail in general for this model, but a weaker monotonicity property does hold: the average edge density is increasing in p.

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Primary Subjects: 60K35, 82B43, 60J10

Keywords: Conditional percolation; stochastic domination; one-dimensional lattice; Markov chain

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Permanent link to this document: http://projecteuclid.org/euclid.aap/1261669588
Digital Object Identifier: doi:10.1239/aap/1261669588
Zentralblatt MATH identifier: 05706692
Mathematical Reviews number (MathSciNet): MR2663238

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