Rafaël Digneaux - PhD Student in Lille
Welcome to the website of Rafaël Digneaux, here you will find my research interest, preprints, academic background, and more.
Contact
You can find me in Lille, at laboratoire Paul Painlevé, M3 building, office 320 (3rd floor), and by email at rafael.digneaux[at]univ-lille.fr or rafael.digneaux[at]ens-paris-saclay.fr.
About my thesis
Since September 2024, I have been a PhD student at Université de Lille, under the supervision of David Dereudre (professor). My thesis is titled:
"Rigidity of Riesz gas and dependent perturbed lattices".
The goal of this thesis is to establish rigidity properties (number-rigidity, hyperuniformity, crystallization) rigorously for Riesz gases. These gases are infinite point processes defined in dimension d, and with homogeneity parameter s, by following the interaction potential |x|^{-s} if s>0 (singular case), and -|x|^{-s} if s<0 (non-singular case).
Right now, I'm specifically interested in the links between DLR equations and number-rigidity, or non-number-rigidity.
Interests
Topics: probability, stochastic geometry, point processes, statistical physics
Precise keywords: rigidities, number-rigidity, hyperuniformity, crystallization, Riesz gases, Gibbs measures, DLR equations
Curriculum Vitae
I graduated from École Normale Supérieure Paris-Saclay (formerly in Cachan) and from Université Paris-Saclay in 2024, where I completed the Master 2 program in Probability and Statistics (Orsay). Prior to that, I passed the "agrégation" in maths in 2023 (ranked 13th). I did my "prépa" at lycée Montaigne (Bordeaux).
Preprints and papers
[1] "Rigidity of one-dimensional point processes via optimal transport", David Dereudre, Rafaël Digneaux (pdf)
Conferences attended
2025-2026
Points configurations: stat. physics & potential theory (Marseille)
Point Processes and Applications (Lille)
2024-2025
GeoSto2025 (Grenoble)
GrHyDy, random spatial models (Lille)
Talks
2025-2026
Points configurations: stat. physics & potential theory, Marseille, "Rigidity of long-range Gibbs point processes" (~10mn)
PhD student seminar IMT, Toulouse, "Rigidity of random point configurations" (~1h)
Working group on point processes, Lille, "Rigidity of Riesz gases" (~2h)
2024-2025
Working group on point processes, Lille, "Optimal transport of stationary point processes" (~2h)
Teaching
2025-2026
L2: discrete probabilities
L2: numerical methods (Python)
L2: generalized integrals & Fourier series
M2: estimation statistics & Markov chains (Matlab, Python) at IMT Nord Europe
2024-2025
L2: discrete probabilities
L1: general mathematics
In 2023-2024, I was "khôlleur" in MP* at lycée Blaise Pascal (Orsay).
Agrégation
J'ai passé l'agrégation en 2023 (classé 13ème) après la prépa agreg de l'ENS Paris-Saclay. Vous pouvez retrouver l'ensemble de mes développements tapés (avec le tableau des couplages entre toutes les leçons), et mon retour sur les oraux.
