S'ebastien Martineau

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20182025

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7 papers · 1 filter

math.PR2025

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…

math.PR2025

Percolative properties of the random coprime colouring

Samuel Le Fourn, Mike Liu, Sébastien Martineau

Given $u$ and $v$ in $Z^{d}$ , say that $u$ is visible from $v$ if the segment from $u$ to $v$ contains exactly two elements, which are $u$ and $v$ . Take $X$ "uniformly at ra…

math.PR2025

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 $p$ . Seeing all this and possib…

math.PR2022

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 $p_{c}$ of a graph satisfying $p_{c} < 1$ depends only on its local structure. In this note, we…

math.PR2020

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 $L^{d} = (Z^{d}, E^{d})$ be the $d$ -dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on $ \mathbb{L}^{…

math.PR2018

On coprime percolation, the visibility graphon, and the local limit of the GCD profile

Sébastien Martineau

Colour an element of $Z^{d}$ white if its coordinates are coprime and black otherwise. What does this colouring look like when seen from a "uniformly chosen" point of $\math…