Research interests
I am currently assistant professor (maître de conférences) at the Department of Mathematics of the University Paris-Sud (Orsay, France), and I am working in the team Probability and Statistics. Here is a detailed curriculum vitæ: in French and in English.
My works focus on the use of techniques from harmonic analysis in the study of large random objects. More precisely, the two main directions of my researches are:
- → convergence of random variables. With my collaborators, we developed the theory of mod-ϕ convergence, which refines the central limit theorems and leads to large deviation principles, Berry-Esseen estimates, local limit theorems, etc. This theory allowed us to extend the classical probabilistic results on sums of i.i.d. to numerous other sequences of random variables, including: sums of random variables with a sparse dependency graph, characteristic polynomials of random matrices, functionals of a Markov chain, magnetisation of the Ising model, statistics of random graphs or permutations, arithmetic functions of a random integer.
- → random objects on groups and symmetric spaces. I study random processes, random graphs and random combinatorial structures that are drawn on groups (finite, discrete or Lie) and their quotients, by using their (asymptotic) representation theory. These works are also connected to algebraic combinatorics, random matrix theory, free probability, and interacting systems of particles.
