4 papers
Locality of percolation for graphs with polynomial growth
Daniel Contreras, Sébastien Martineau, Vincent Tassion
Schramm's Locality Conjecture asserts that the value of the critical percolation parameter of a graph satisfying depends only on its local structure. In this note, we…
Approximation on slabs and uniqueness for inhomogeneous percolation with a plane of defects
Bernardo N. B. de Lima, Sébastien Martineau, Humberto C. Sanna +1
Let be the -dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on $ \mathbb{L}^{…
On coprime percolation, the visibility graphon, and the local limit of the GCD profile
Sébastien Martineau
Colour an element of white if its coordinates are coprime and black otherwise. What does this colouring look like when seen from a "uniformly chosen" point of $\math…
Strict monotonicity of percolation thresholds under covering maps
Sébastien Martineau, Franco Severo
We answer a question of Benjamini and Schramm by proving that under reasonable conditions, quotienting a graph strictly increases the value of its percolation critical parameter $p…