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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 and in English. Here is also a research statement: 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 (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):

- Fluctuations of the Gromov-Hausdorff sample model, with J. De Catelan. Submitted.
- Asymptotic representation theory and the spectrum of a random geometric graph on a compact Lie group.
*Electronic Journal of Probability*, 24(43):1-85, 2019. - Graphons, permutons and the Thoma simplex: three mod-Gaussian moduli spaces, with V. Féray and A. Nikeghbali.
*Proceedings of the London Mathematical Society*, 121(4):876-926, 2020. - Mod-ϕ convergence: Approximation of discrete measures and harmonic analysis on the torus, with R. Chhaibi, F. Delbaen and A. Nikeghbali. To appear in
*Ann. Institut Fourier*. - Local limit theorems and mod-ϕ convergence, with M. dal Borgo and A. Nikeghbali.
*Latin American Journal of Probability and Mathematical Statistics*, 16(1):817-853, 2019. - Mod-ϕ convergence, II: Estimates on the speed of convergence, with V. Féray and A. Nikeghbali.
*Séminaire de Probabilités L*, 405-478, LNM 2252, Springer-Verlag, 2019. - Representation Theory of Symmetric Groups.
*Discrete Mathematics and Applications*, 666+xvi p., CRC Press, 2017. More details here.

- Mod-ϕ convergence. Normality Zones and Precise Deviations, with V. Féray and A. Nikeghbali.
*Springer Briefs in Probability and Mathematical Statistics,*152+xii p., Springer-Verlag, 2016.

- Mod-Gaussian convergence and its applications for models of statistical mechanics, with A. Nikeghbali.
*In Memoriam Marc Yor - Séminaire de Probabilités XLVII*, 369-425, LNM 2137, Springer-Verlag, 2015. - The cut-off phenomenon for Brownian motions on compact symmetric spaces,
*Potential Analysis*, 40(4):427-509, 2014. - Partial isomorphisms over finite fields,
*Journal of Algebraic Combinatorics*, 40(1):83-136, 2014. - Fluctuations of central measures on partitions,
*Proceedings of the 24th International Conference on Formal Power Series and Algebraic Combinatorics (Nagoya, Japan)*, p. 387-398, 2012. - Kerov’s central limit theorem for Schur-Weyl and Gelfand measures,
*Proceedings of the 23rd International Conference on Formal Power Series and Algebraic Combinatorics (Reykjavík, Iceland)*, p. 669-680, 2011. - Products of Geck-Rouquier conjugacy classes and the algebra of composed permutations,
*Proceedings of the 22nd International Conference on Formal Power Series and Algebraic Combinatorics (San Francisco, USA)*, p. 789-800, 2010. - Asymptotics of q-Plancherel measures, with V. Féray,
*Probability Theory and Related Fields*, 152(3-4):589-624, 2012.

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:

- Mod-ϕ convergence, III: Multi-dimensional mod-Gaussian convergence and related estimates of probabilities, with V. Féray and A. Nikeghbali. We extend the results of the two previous papers to the setting of multi-dimensional mod-Gaussian convergence. This extension relies on some intricate geometrical arguments, which are required in order to control the convergence in law to the Gaussian distribution, and the precise moderate deviations of the multi-dimensional models.

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:

- The theory of graphons and permutons.
- Determinantal point processes and applications.
- Random compression of an integer partition.

Academic works

- Memoir of my
*habilitation à diriger des recherches (2018)*: Techniques of harmonic analysis and asymptotic results in probability theory, 166 pages, in English (with an abstract in French). - Memoir of my Ph. D. thesis (2007-2010, under the supervision of Philippe Biane): Random partitions and asymptotic theory of symmetric groups, Hecke algebras and finite Chevalley groups, 300 pages, in French.