{"id":9,"date":"2019-11-26T03:13:21","date_gmt":"2019-11-26T02:13:21","guid":{"rendered":"http:\/\/guillaume-ck.com\/?page_id=9"},"modified":"2025-11-13T15:13:55","modified_gmt":"2025-11-13T14:13:55","slug":"research","status":"publish","type":"page","link":"https:\/\/guillaume-ck.com\/index.php\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n

My research mainly focuses on discrete probability objects and their scaling limits.
A few keywords: sparse random graphs, branching processes, mixing times of Markov chains, the Gaussian free field, interacting particle systems, random walks in strongly-correlated environments, sharpness of phase transitions.
My collaborators include: Arthur Blanc-Renaudie<\/a>, Camille Cazaux<\/a>, Christina Goldschmidt<\/a>, Daniel Kious<\/a>, Tanguy Lions<\/a>, C\u00e9cile Mailler<\/a>, Pierre-Fran\u00e7ois Rodriguez<\/a>, Arvind Singh<\/a>. <\/p>\n\n\n\n

Selected papers<\/h3>\n\n\n\n

2024 Sharp threshold for the ballisticity of the random walk on the exclusion process<\/a><\/em>, Conchon–Kerjan Guillaume, Kious Daniel and Rodriguez Pierre-Fran\u00e7ois. In revision for the Journal of the European Mathematical Society.
<\/p>\n\n\n\n

2023 The stable graph: the metric space scaling limit of a critical random graph with i.i.d. power-law degrees<\/a><\/em>, Conchon–Kerjan Guillaume and Goldschmidt Christina, The Annals of Probability 51(1): 1-69 (January 2023). DOI: 10.1214\/22-AOP158.<\/p>\n\n\n\n

2019 Cutoff for random lifts of weighted graphs<\/a><\/em>, Conchon–Kerjan Guillaume,
The Annals of Probability 50(1): 304-338 (January 2022). DOI: 10.1214\/21-AOP1534.<\/p>\n\n\n\n

Other works<\/h3>\n\n\n\n

2024 A phase transition for the biased tree-builder random walk<\/em><\/a>, Blanc-Renaudie Arthur, Cazaux Camille, Conchon–Kerjan Guillaume, Lions Tanguy and Singh Arvind. In revision for the Electronic Journal of Probability.

2023 Anatomy of a gaussian giant: supercritical level-sets of the free field on regular random graphs<\/a><\/em>, Conchon–kerjan Guillaume, Electronic Journal of Probability, 28:1-60 (2023). DOI: 10.1214\/23-EJP920

2023 Scaling limit of critical random trees in random environment<\/em><\/a>, Conchon–Kerjan Guillaume, Kious Daniel and Mailler C\u00e9cile, Electronic Journal of Probability, 29: 1-53 (2024). DOI: 10.1214\/24-EJP1139<\/p>\n\n\n\n

2023 Speed of the random walk on the supercritical Gaussian Free Field percolation on regular trees<\/em><\/a>, Conchon–Kerjan Guillaume. In revision for the Annals of Applied Probability.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Grants<\/h3>\n\n\n\n

New Investigator Award: ‘New Phenomena for Random Walks in Dynamic Environments’, 2026-2029.
<\/p>\n\n\n\n

<\/p>\n\n\n\n

Talks<\/strong><\/h3>\n\n\n\n

June 2025 Conference Phase Transitions and Dynamics in Random Media, McGill, Montr\u00e9al
Talk: \u00ab\u00a0Sharpness for the speed of the random walk on the simple exclusion process\u00a0\u00bb<\/p>\n\n\n\n

May 2025 S\u00e9minaire de Probabilit\u00e9s, LPSM Paris
Talk: \u00ab\u00a0The random walk on the exclusion process: a Law of Large numbers in dimensions >= 5\u00a0\u00bb

April 2025 Online Probability Seminar
Double-talk: \u00ab\u00a0Sharpness for the speed of the random walk on the simple exclusion process\u00a0\u00bb
jointly with Daniel Kious<\/p>\n\n\n\n

April 2025 Conference Branching and Persistence, Angers
Talk: \u00ab\u00a0A phase transition for the tree-builder random walk\u00a0\u00bb<\/p>\n\n\n\n

January 2025 Probability seminar, NTU Taipei
Talk: \u00ab\u00a0A sharpness phenomenon for a random walk driven by the exclusion process\u00a0\u00bb

June 2024 Probability seminar, University of Oxford
Talk: \u00ab\u00a0Sharpness for the speed of the random walk on the simple exclusion process\u00a0\u00bb<\/p>\n\n\n\n

February 2024 MAS Seminar, University of Sussex
Talk: \u00ab\u00a0The monotonic speed of the random walk on the simple exclusion process\u00a0\u00bb

January 2024, CUWB conference, Playa del Carmen
Talk:\u00a0\u00bbThe monotonic speed of the random walk on the simple exclusion process\u00a0\u00bb

July 2023 XVI CLAPEM<\/a> (Latin American Congress of Probability and Mathematical Statistics), S\u00e3o Paulo, invited session
Talk: \u00ab\u00a0Speed of the random walk on the simple exclusion process\u00a0\u00bb<\/p>\n\n\n\n

March 2023 London Analysis and Probability Seminar, Imperial College
Talk: \u00ab\u00a0A Gaussian cousin to the Erd\u0151s\u2013R\u00e9nyi graph\u00a0\u00bb<\/p>\n\n\n\n

March 2023 Probability Seminar, King’s College London
Talk: \u00ab\u00a0Gaussian Free Field percolation on regular graphs: a cousin of Erd\u00f6s-R\u00e9nyi\u00a0\u00bb<\/p>\n\n\n\n

December 2022 Probability Seminar Series, University of Sheffield
Talk: \u00ab\u00a0Scaling limit of a branching process in a varying environment\u00a0\u00bb<\/p>\n\n\n\n

October 2022 Probability Seminar, University of Cambridge
Talk: \u00ab\u00a0Scaling limit of a branching process in a varying environment\u00a0\u00bb<\/p>\n\n\n\n

June 2022 Stochastic Processes and Applications, Wuhan, Invited session Mixing times of Markov chains<\/em>
Talk: \u00ab\u00a0Entropic cutoff for the random walk on random lifts of Markov chains\u00a0\u00bb<\/p>\n\n\n\n

June 2022 Probability Seminar, University of Oxford
Talk: \u00ab\u00a0Scaling limit of a branching process in a varying environment\u00a0\u00bb<\/p>\n\n\n\n

May 2022 Probability Seminar, University of Cologne
Talk: \u00ab\u00a0Scaling limit of a critical Galton-Watson tree in random environment\u00a0\u00bb<\/p>\n\n\n\n

May 2021 Seminar in Probability Theory and Statistics, Universit\u00e4t Basel.
Talk: \u00ab\u00a0Level-set percolation of the GFF on regular graphs: emergence of a Gaussian giant\u00a0\u00bb<\/p>\n\n\n\n

July 2019 Random Trees and Graphs Summer School<\/a>, CIRM, Marseille.
Talk: \u00ab\u00a0Cutoff for the random walk on random lifts\u00a0\u00bb

June 2019 Les Probabilit\u00e9s de Demain, Universit\u00e9 Paris-Diderot.
Talk: \u00ab\u00a0Cutoff for the random walk on lifts of graphs\u00a0\u00bb

July 2018 Saint-Flour Probability Summer School.
Talk: \u00ab\u00a0Metric scaling limit for a critical configuration model with power-law degrees\u00a0\u00bb

May 2018 Franco-Dutch YEP Workshop<\/a>, TU Eindhoven, Netherlands.
Talk: \u00ab\u00a0Metric scaling limit for a critical configuration model with power-law degrees\u00a0\u00bb
<\/p>\n\n\n\n

Other conferences<\/strong>

November 2021 The Cutoff Phenomenon for Finite Markov Chains<\/a>, Oberwolfach, Germany

January 2018 Young Probabilists and Statisticians<\/a>, IHP, Paris<\/p>\n\n\n\n

July 2017 Spectral properties of large random objects<\/a>, IHES, France<\/p>\n\n\n\n

March 2017 Journ\u00e9es ALEA<\/a>, CIRM, Marseille<\/p>\n\n\n\n

July 2016 Saint-Flour Probability Summer School

June 2015 PIMS Summer School<\/a>, McGill University, Montr\u00e9al<\/p>\n\n\n\n




<\/p>\n\n\n\n


<\/p>\n","protected":false},"excerpt":{"rendered":"

My research mainly focuses on discrete probability objects and their scaling limits. A few keywords: sparse random graphs, branching processes, mixing times of Markov chains, the Gaussian free field, interacting particle systems, random walks in strongly-correlated environments, sharpness of phase transitions. My collaborators include: Arthur Blanc-Renaudie, Camille Cazaux, Christina Goldschmidt, Daniel Kious, Tanguy Lions, C\u00e9cile […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-9","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/pages\/9","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/comments?post=9"}],"version-history":[{"count":37,"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/pages\/9\/revisions"}],"predecessor-version":[{"id":753,"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/pages\/9\/revisions\/753"}],"wp:attachment":[{"href":"https:\/\/guillaume-ck.com\/index.php\/wp-json\/wp\/v2\/media?parent=9"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}