Does Eulerian percolation on $Z^2$ percolate ?

Olivier Garet (1) , Regine Marchand (1) , Irène Marcovici (1)

1 IECL - Institut Élie Cartan de Lorraine

Eulerian percolation on Z 2 with parameter p is the classical Bernoulli bond percolation with parameter p conditioned on the fact that every site has an even degree. We first explain why Eulerian percolation with parameter p coincides with the contours of the Ising model for a well-chosen parameter β(p). Then we study the percolation properties of Eulerian percolation.

Domaines: Probabilités [math.PR]

Olivier Garet, Regine Marchand, Irène Marcovici. Does Eulerian percolation on $Z^2$ percolate ?. 2017. ⟨hal-01342910v3⟩