My research mainly focuses on sparse random graphs and Markov chains, and on how to derive global properties (scaling limits, mixing times for random walks, percolation) on those structures.

### Publications

2019 *Cutoff for random lifts of weighted graphs*, Conchon–Kerjan Guillaume,

The Annals of Probability 50(1): 304-338 (January 2022). DOI: 10.1214/21-AOP1534.

### Preprints

2021 *Anatomy of a gaussian giant: supercritical level-sets of the free field on regular random graphs*, Conchon–Kerjan Guillaume (submitted).

2020 *The stable graph: the metric space scaling limit of a critical random graph with i.i.d. power-law degrees*, Conchon–Kerjan Guillaume and Goldschmidt Christina (in revision for The Annals of Probability).

**Talks and conferences**

May 2021 Seminar in Probability Theory and Statistics, Universität Basel.

Talk: « Level-set percolation of the GFF on regular graphs: emergence of a Gaussian giant »

July 2019 Random Trees and Graphs Summer School, CIRM, Marseille.

Talk: « Cutoff for the random walk on random lifts »

June 2019 Les Probabilités de Demain, Université Paris-Diderot.

Talk: « Cutoff for the random walk on lifts of graphs »

July 2018 Saint-Flour Probability Summer School.

Talk: « Metric scaling limit for a critical configuration model with power-law degrees »

May 2018 Franco-Dutch YEP Workshop, TU Eindhoven, Netherlands.

Talk: « Metric scaling limit for a critical configuration model with power-law degrees »

January 2018 Young Probabilists and Statisticians, IHP, Paris

July 2017 Spectral properties of large random objects, IHES, France

March 2017 Journées ALEA, CIRM, Marseille

July 2016 Saint-Flour Probability Summer School

June 2015 PIMS Summer School, McGill University, Montréal