Research

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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).

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 (V. Féray, A. Nikeghbali, R. Chhaibi,… the list is growing rapidly!), 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.

Publications

My list of publications so far (click on a title to get the pdf):

Slides / works in progress

Slides of my presentation for the defense of my habilitation à diriger des recherches.

Slides of a talk on fluctuations and concentration inequalities for central measures on integer partitions (in French).

Slides of a recent talk on the spectrum of random geometric graphs on symmetric spaces (in French).

Slides of another recent talk on mod-Gaussian convergence for graphon models.

I usually put my papers on arXiv, but I put here some works that are well advanced but not yet arxivable:

Surveys

I sometimes write an informal survey of a topic in mathematics, in order to prepare myself for my researches. These documents are not meant to be published, but they might provide an easy introduction to some objects:

Academic works