Research interests

I am interested in the interplay between statistical mechanics and other fields, including number theory and the ergodic and geometric aspects of group theory. My favourite model of statistical mechanics is percolation, which simply consists in keeping or erasing each elementary constituent of your geometric medium independently with some retention probability \(p\). There is a critical value for \(p\), which is called \(p_c\). Below this critical value, the medium breaks into dust while above it, the medium keeps its properties. This phenomenon is strongly related to the phase transitions encountered in physics.

Supercritical percolation

with Daniel Contreras and Vincent Tassion

We study supercritical percolation on homogeneous graphs of polynomial growth.
Duke Mathematical Journal, 2024

Polynomial locality

with Daniel Contreras and Vincent Tassion

Using , we prove Schramm's Locality Conjecture under the assumption of polynomial growth.
Electronic Communications in Probability, 2023

The coprime colouring

Plant a forest with one thin tree at each vertex of \(\mathbb{Z}^d\). Then pick a tree "uniformly at random" and replace it by a lamp. Which are the trees lit by the lamp?
Electronic Communications in Probability, 2022

Inhomogeneous percolation

with Bernardo de Lima, Humberto Sanna, and Daniel Valesin

We investigate percolation on \(\mathbb{Z}^d\) with a sublattice of defects.
ALEA, 2022

Strict monotonicity

with Franco Severo

We show that taking strict quotients of graphs with \(p_c<1\) strictly increases the value of \(p_c\). This answers Question 1 of the Percolation beyond \(\mathbb{Z}^d\) paper of Benjamini and Schramm.
Annals of Probability, 2019

Abelian locality

with Vincent Tassion

We prove Schramm's Locality Conjecture in the particular case of Cayley graphs of abelian groups.
Annals of Probability, 2017

Many connective constants

This article proves that the set of connective constants of Cayley graphs contains a Cantor set.
Electronic Communications in Probability, 2017

Directed DLA

This paper investigates a model midway between ballistic deposition and diffusion-limited aggregation.
ALEA, 2017

Locally infinite graphs

This paper investigates the geometry of homogeneous locally infinite graphs.
The Graduate Journal of Mathematics, 2017

Rotarily transitive graphs

Cayley graphs are graphs that are homogeneous due to translations. Can a graph be homogeneous due to rotations?
ArXiv, 2016

Ergodicity and indistinguishability

We review the dictionary translating between orbit equivalence and percolation, and add a new word to it.
L'Enseignement Mathématique, 2015