Dominique Malicet
Associate professor (Maître de conférences) of Mathematics
Université Gustave Eiffel, LAMA
email: dominique.malicet[at]univ-eiffel.fr

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Topics of research


-Dynamical systems and ergodic theory:
I am interested in the study of group actions and random dynamical sysytems on manifolds of small dimension. I am trying to exhibit hyperbolicity phenomena (e.g. study of the Lyapunov exponents), conditions of reduction (e.g. KAM reduction, invariance principles) and structure of group actions (e.g. Markov partitions, Ping-pong structures).

-Functional analysis in probability:
I am working in the study of non linear functionals of random variables by the mean of functional calculus technics (e.g. Dirichlet and Malliavin's calculus, Wiener's chaos decompositions), in particular to establish properties of the distribution measures, concentration and anticoncentration phenomena, central limit theorems.


ANR project

I participated to the ANR project Gromeov, on the study of group actions on manifolds of small dimensions, supervised by Michele Triestino and Victor Kleptsyn between 2019 and 2024.


Responsabilities

I organize the analysis seminar of the LAMA with Colin Petitjean [page].


Publications


1-"Properties of convergence in Dirichlet structures", Journal of Functional Analysis, 2013, vol. 264, no 9, p. 2077-2096. With Guillaume Poly.
[Journal]
2-"Generalization of the Nualart–Peccati criterion", The Annals of Probability, 2016, vol. 44, no 2, p. 924-954. With Ehsan Azmoodeh, Guillaume Mijoule and Guillaume Poly.
[Journal] [arxiv]
3-"Squared chaotic random variables: new moment inequalities with applications", Journal of Functional Analysis, 2016, vol. 270, no 2, p. 649-670. With Ivan Nourdin, Giovanni Peccati and Guillaume Poly.
[Journal] [arxiv]
4-"Random walks on Homeo(S1)", Communications in Mathematical Physics, 2017, vol. 356, p. 1083-1116.
[Journal] [arxiv]
5-"Expanding actions: minimality and ergodicity", Stochastics and Dynamics, 2017, vol. 17, no 04. With Pablo G. Barrientos, Abbas Fakhari and Aliasghar Sarizadeh.
[Journal] [arxiv]
6-"On the chaos game of iterated function systems", Topological Methods in Nonlinear Analysis, 2017, vol. 49, no 1, p.105-132. With Pablo G. Barrientos, Fatemeh H. Ghane, Aliasghar Sarizadeh.
[Journal] [arxiv]
7-"Groups with infinitely many ends acting analytically on the circle", Journal of topology, 2019, vol. 12, no 4, p. 1315-1367. With Sébastien Alvarez, Dmitry Filimonov, Victor Kleptsyn, Carlos Meniño, Andrés Navas and Michele Triestino.
[Journal] [arxiv]
8-"Ping-pong configurations and circular orders on free groups", Groups, Geometry, and Dynamics, 2019, vol. 13, no 4, p. 1195-1218. With Kathryn Mann, Cristòbal Rivas, Michele Triestino.
[Journal] [arxiv]
9-"Extremal exponents of random products of conservative diffeomorphisms", Mathematische Zeitschrift, 2020, vol. 296, no 3-4, p. 1185-1207. With Pablo G. Barrientos.
[Journal] [arxiv]
10-"Lyapunov exponent of random dynamical systems on the circle", Ergodic Theory and Dynamical Systems, 2022, vol. 42, no 6, p. 2080-2107.
[Journal] [arxiv]
11-"Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction", Journal of Combinatorial Algebra, 2023, vol. 8, no 1, p. 57-109. With Juan Alonso, Sébastien Alvarez, Carlos M. Cotón and Michele Triestino.
[Journal] [arxiv]
12-"Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications", Commentarii Mathematici Helvetici, 2023, vol. 98 , no 4 , p. 643-691. With Sébastien Alvarez, Pablo G. Barrientos, Carlos M. Cotón, Dmitry Filimonov, Victor Kleptsyn and Michele Triestino.
[Journal] [arxiv]
13-"Almost sure behavior of the critical points of random polynomials", Bulletin of London Mathematical Society, 2024, vol. 56, no 2, p. 767-782. With Jürgen Angst and Guillaume Poly.
[Journal] [arxiv]
14-"A short proof of the strong three dimensional Gaussian product inequality", Proceedings of the American Mathematical Society, 2024, vol. 152, no 1, p. 403-409. With Ronan Herry and Guillaume Poly.
[Journal] [arxiv]
15-"Superconvergence phenomenon in Wiener chaoses", Annals of Probability, 2024, vol. 52, no 3, p. 1162-1200. With Ronan Herry and Guillaume Poly.
[Journal] [arxiv]
16-"Regularity of laws via Dirichlet forms--Application to quadratic forms in independent and identically distributed random variables", Probability Theory and Related Fields, 2024. With Ronan Herry and Guillaume Poly.
[Journal] [arxiv]

Preprints


1-"Groups of smooth diffeomorphisms of Cantor sets embedded in a line", 2023. With Emmanuel Militon. Accepted in Annales de l'institut Fourier.
[arxiv]
2-"Random actions homeomorphisms of Cantor sets embedded in a line and Tits alternative", 2023. With Emmanuel Militon.
[arxiv]
3-"Sharp total variation rates of convergence for fluctuations of linear statistics of ß-ensembles", 2024. With Jürgen Angst, Ronan Herry and Guillaume Poly.
[arxiv]
4-"Limit distributions for polynomials with independent and identically distributed entries", 2024. With Ronan Herry and Guillaume Poly.
[arxiv]
5-"Mostly contracting random maps", 2024. With Pablo G. Barrientos.
[arxiv]
6-"Random Dynamical Systems on the circle without a finite orbit", 2025. With Graccyela Salcedo.
[arxiv]


PhD thesis

Title: Exposants de Lyapunov de systemes dynamiques aleatoires sur le tore
Advisor: Raphaël Krikorian
Place: Sorbonne Université
Year of defense: 2012
Reviewers: Konstantin Khanin and Jean-Cristophe Yoccoz
Jury: Artur Ávila, Sylvain Crovisier, Dmitry Dolgopyat, Bassam Fayad, Yves Le Jan and Jean-Paul Thouvenot
PDF: [here]


Miscellaneous notes :

-"The 2x-3x theorem of Furstenberg", appendix chapter for the text "Entropy, Lyapunov exponents, and rigidity of group actions" of A.Brown, in Ensaios Matemáticos, 2019, vol. 33
[here], [integral text]
-"Série de Riemann à exposant oscillant", analysis topic for "Concours SMF junior" 2022 (french)
[questions], [solution]



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