# Conditional percolation on one-dimensional lattices Artikel i vetenskaplig tidskrift, 2009

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 $p$.

Conditional percolation

stochastic domination

Markov chains

one-dimensional lattices

## Författare

#### Marina Axelson-Fisk

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

#### Olle Häggström

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik