3 citations · 4 across the 8 of their papers we have counts for
14 papers
Percolation on graphs of polynomial growth is local: analyticity, supercritical sharpness, isoperimetry
Sébastien Martineau, Christoforos Panagiotis
We investigate locality of the supercritical regime for Bernoulli percolation on transitive graphs with polynomial growth, by which we mean the following. Take a transitive graph o…
Percolative properties of the random coprime colouring
Samuel Le Fourn, Mike Liu, Sébastien Martineau
Given and in , say that is visible from if the segment from to contains exactly two elements, which are and . Take "uniformly at ra…
Stochastic domination and lifts of random variables in percolation theory
Sébastien Martineau, Rémy Poudevigne, Paul Rax
Consider some matrix waiting for its coefficients to be written. For each column, sample independently a Bernoulli random variable of some parameter . Seeing all this and possib…
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…
Supercritical percolation on graphs of polynomial growth
Daniel Contreras, Sébastien Martineau, Vincent Tassion
We consider Bernoulli percolation on transitive graphs of polynomial growth. In the subcritical regime (), it is well known that the connection probabilities decay exponenti…
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…
Locally infinite graphs and symmetries
Sébastien Martineau
When one studies geometric properties of graphs, local finiteness is a common implicit assumption, and that of transitivity a frequent explicit one. By compactness arguments, local…
The set of connective constants of Cayley graphs contains a Cantor space
Sébastien Martineau
The purpose of this note is to prove that the set of connective constants of Cayley graphs contains a Cantor space.
On rotarily transitive graphs
Sébastien Martineau
From the point of view of discrete geometry, the class of locally finite transitive graphs is a wide and important one. The subclass of Cayley graphs is of particular interest, as…
Directed Diffusion-Limited Aggregation
Sébastien Martineau
In this paper, we define a directed version of the Diffusion-Limited-Aggregation model. We present several equivalent definitions in finite volume and a definition in infinite volu…
Locality of percolation for abelian Cayley graphs
Sebastien Martineau, Vincent Tassion
We prove that the value of the critical probability for percolation on an abelian Cayley graph is determined by its local structure. This is a partial positive answer to a conjectu…
Ergodicity and indistinguishability in percolation theory
Sébastien Martineau
This paper explores the link between the ergodicity of the clus-ter equivalence relation restricted to its infinite locus and the indis-tinguishability of infinite clusters. It is…