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
2023 Anatomy of a gaussian giant: supercritical level-sets of the free field on regular random graphs, Conchon–kerjan Guillaume, Electronic Journal of Probability, 28:1-60 (2023). DOI: 10.1214/23-EJP920
2023 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, The Annals of Probability 51(1): 1-69 (January 2023). DOI: 10.1214/22-AOP158.
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
2023 Speed of the random walk on the supercritical Gaussian Free Field percolation on regular trees, Conchon–Kerjan Guillaume (submitted).
2022 Scaling limit of critical random trees in random environment, Conchon–Kerjan Guillaume, Kious Daniel and Mailler Cécile (submitted).
Talks
July 2023 XVI CLAPEM (Latin American Congress of Probability and Mathematical Statistics), São Paulo, invited session
Talk: « Speed of the random walk on the simple exclusion process »
March 2023 London Analysis and Probability Seminar, Imperial College
Talk: « A Gaussian cousin to the Erdős–Rényi graph »
March 2023 Probability Seminar, King’s College London
Talk: « Gaussian Free Field percolation on regular graphs: a cousin of Erdös-Rényi »
December 2022 Probability Seminar Series, University of Sheffield
Talk: « Scaling limit of a branching process in a varying environment »
October 2022 Probability Seminar, University of Cambridge
Talk: « Scaling limit of a branching process in a varying environment »
June 2022 Stochastic Processes and Applications, Wuhan, Invited session Mixing times of Markov chains
Talk: « Entropic cutoff for the random walk on random lifts of Markov chains »
June 2022 Probability Seminar, University of Oxford
Talk: « Scaling limit of a branching process in a varying environment »
May 2022 Probability Seminar, University of Cologne
Talk: « Scaling limit of a critical Galton-Watson tree in random environment »
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 »
Other conferences
November 2021 The Cutoff Phenomenon for Finite Markov Chains, Oberwolfach, Germany
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