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# Conditional percolation on one-dimensional lattices

Marina Axelson-Fisk (Institutionen för matematiska vetenskaper) ; Olle Häggström (Institutionen för matematiska vetenskaper, matematisk statistik)
Advances in Applied Probability (0001-8678). Vol. 41 (2009), 4, p. 3395-3415.

Conditioning i.i.d.\ bond percolation with retention parameter $p$ on a one-dimensional periodic lattice on the event of having a bi-infinite path from $-\infty$ to $\infty$ 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 $p$.

Nyckelord: Conditional percolation, stochastic domination, one-dimensional lattices, Markov chains

CPL Pubid: 102536

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Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)
Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)