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Conditional percolation on one-dimensional lattices

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

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

Denna post skapades 2009-12-01. Senast ändrad 2017-07-03.
CPL Pubid: 102536


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Institutioner (Chalmers)

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


Matematisk statistik

Chalmers infrastruktur